## Numerical Linear Algebra with Applications

 Short Title: Numer. Linear Algebra Appl. Publisher: Wiley, Chichester ISSN: 1070-5325; 1099-1506/e Online: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506 Comments: Published electronic only as of Vol. 19 (2012). Print ISSN until then: 1070-5325.
 Documents Indexed: 1,390 Publications (since 1994) References Indexed: 973 Publications with 24,525 References.
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### Authors

 28 Vassilevski, Panayot Spirov 27 Ng, Michael Kwok-Po 26 Axelsson, Axel Owe Holger 23 Reichel, Lothar 23 Saad, Yousef 23 Wei, Yimin 20 Bai, Zhongzhi 18 Manteuffel, Thomas A. 18 Serra-Capizzano, Stefano 16 MacLachlan, Scott P. 15 Qi, Liqun 13 McCormick, Steve Fahrney 12 Notay, Yvan 12 Simoncini, Valeria 11 Peña, Juan Manuel 10 Bergamaschi, Luca 10 Blaheta, Radim 10 Margenov, Svetozar D. 10 Scott, Jennifer A. 9 De Sterck, Hans 9 Khoromskiĭ, Boris Nikolaevich 9 Neytcheva, Maya G. 9 Noschese, Silvia 9 Poloni, Federico G. 9 Szyld, Daniel B. 9 Wathen, Andrew John 8 Donatelli, Marco 8 Gratton, Serge 8 Huang, Ting-Zhu 8 Kaporin, Igor E. 8 Meerbergen, Karl 8 Oosterlee, Cornelis Willebrordus 8 Ruge, J. 8 Van Huffel, Sabine 8 Yavneh, Irad 8 Zikatanov, Ludmil T. 7 Chan, Raymond Hon-Fu 7 Cvetković, Ljiljana 7 Falgout, Robert D. 7 Giraud, Luc 7 Greif, Chen 7 Kraus, Johannes K. 7 Lazarov, Raytcho D. 7 Lin, Wen-Wei 7 Mehrmann, Volker 6 Benner, Peter 6 Benzi, Michele 6 Brezina, Marian 6 Bunch, James R. 6 Ching, Wai-Ki 6 Diao, Huaian 6 Dostál, Zdeněk 6 Gustafsson, Ivar 6 Kolotilina, Lily Yu. 6 Kostić, Vladimir R. 6 Kressner, Daniel 6 Lee, Barry 6 Li, Wen 6 Marek, Ivo 6 Mastronardi, Nicola 6 Olson, Luke N. 6 Pasciak, Joseph E. 6 Pultarová, Ivana 6 Rüde, Ulrich 6 Sun, Haiwei 6 Tablino Possio, Cristina 6 Vuik, Cornelis 6 Wu, Gang 6 Xiang, Hua 6 Yeremin, A. Yu. 5 Brannick, James J. 5 Cai, Xiao-Chuan 5 Dai, Yu-Hong 5 Duff, Iain S. 5 Garanzha, Vladimir A. 5 Gaspar, Francisco José 5 Gemignani, Luca 5 Grasedyck, Lars 5 Gustafson, Karl Edwin 5 Hayami, Ken 5 He, Yunhui 5 Kolev, Tzanio V. 5 Lindskog, Gunhild 5 Martínez, Ángeles 5 Nagy, James Gerard 5 Nataf, Frédéric 5 Pearson, John W. 5 Shu, Shi 5 Tůma, Miroslav 5 Tuminaro, Raymond S. 5 Tyrtyshnikov, Evgeniĭ Evgen’evich 5 Van Barel, Marc 5 Van der Vorst, Henk Albertus 5 Xu, Jinchao 4 Amat, Sergio P. 4 Bai, Zhengjian 4 Bini, Dario Andrea 4 Björck, Åke 4 Cao, Zhihao 4 Chan, Tony Fan-Cheong ...and 1,736 more Authors
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### Fields

 1,292 Numerical analysis (65-XX) 328 Linear and multilinear algebra; matrix theory (15-XX) 208 Partial differential equations (35-XX) 69 Operations research, mathematical programming (90-XX) 65 Fluid mechanics (76-XX) 62 Mechanics of deformable solids (74-XX) 40 Systems theory; control (93-XX) 36 Probability theory and stochastic processes (60-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 31 Ordinary differential equations (34-XX) 30 Computer science (68-XX) 29 General and overarching topics; collections (00-XX) 29 Information and communication theory, circuits (94-XX) 22 Combinatorics (05-XX) 21 Statistics (62-XX) 20 Optics, electromagnetic theory (78-XX) 17 Operator theory (47-XX) 16 Biology and other natural sciences (92-XX) 9 Quantum theory (81-XX) 9 Statistical mechanics, structure of matter (82-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Integral equations (45-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Geophysics (86-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of particles and systems (70-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Functional analysis (46-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Algebraic geometry (14-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Differential geometry (53-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

1,130 Publications have been cited 11,066 times in 7,032 Documents Cited by Year
Modulus-based matrix splitting iteration methods for linear complementarity problems. Zbl 1240.65181
Bai, Zhong-Zhi
2010
ILUT: A dual threshold incomplete LU factorization. Zbl 0838.65026
1994
Optimal parameters in the HSS-like methods for saddle-point problems. Zbl 1224.65081
Bai, Zhong-Zhi
2009
On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097
Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
2007
Recent computational developments in Krylov subspace methods for linear systems. Zbl 1199.65112
Simoncini, Valeria; Szyld, Daniel B.
2007
Real valued iterative methods for solving complex symmetric linear systems. Zbl 1051.65025
Axelsson, Owe; Kucherov, Andrey
2000
Preconditioning discretizations of systems of partial differential equations. Zbl 1249.65246
Mardal, Kent-Andre; Winther, Ragnar
2011
Fast algorithms for hierarchically semiseparable matrices. Zbl 1240.65087
Xia, Jianlin; Chandrasekaran, Shivkumar; Gu, Ming; Li, Xiaoye S.
2010
A scalable dual-primal domain decomposition method. Zbl 1051.65119
Farhat, Charbel; Lesoinne, Michael; Pierson, Kendall
2000
Convergence of a balancing domain decomposition by constraints and energy minimization. Zbl 1071.65558
Mandel, Jan; Dohrmann, Clark R.
2003
A modified modulus method for symmetric positive-definite linear complementarity problems. Zbl 1224.65152
Dong, Jun-Liang; Jiang, Mei-Qun
2009
Modulus-based synchronous multisplitting iteration methods for linear complementarity problems. Zbl 1313.65131
Bai, Zhong-Zhi; Zhang, Li-Li
2013
Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. Zbl 1212.65245
Benner, P.; Li, J.-R.; Penzl, T.
2008
Approximate solutions and eigenvalue bounds from Krylov subspaces. Zbl 0831.65036
Paige, Chris C.; Parlett, Beresford N.; van der Vorst, Henk A.
1995
New eigenvalue inclusion sets for tensors. Zbl 1324.15026
Li, Chaoqian; Li, Yaotang; Kong, Xu
2014
A projection method to solve linear systems in tensor format. Zbl 1289.65049
Ballani, Jonas; Grasedyck, Lars
2013
A new approximation of the Schur complement in preconditioners for PDE-constrained optimization. Zbl 1274.65187
Pearson, John W.; Wathen, Andrew J.
2012
Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations. Zbl 1051.65038
Perugia, I.; Simoncini, V.
2000
GMRESR: A family of nested GMRES methods. Zbl 0839.65040
Van der Vorst, H. A.; Vuik, C.
1994
A practical method for computing the largest $$M$$-eigenvalue of a fourth-order partially symmetric tensor. Zbl 1224.65101
Wang, Yiju; Qi, Liqun; Zhang, Xinzhen
2009
A survey on the spectral theory of nonnegative tensors. Zbl 1313.15015
Chang, Kungching; Qi, Liqun; Zhang, Tan
2013
Two classes of multisecant methods for nonlinear acceleration. Zbl 1224.65134
2009
The $$Z$$-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory. Zbl 1313.65081
Li, Guoyin; Qi, Liqun; Yu, Gaohang
2013
Deflated and augmented Krylov subspace techniques. Zbl 0889.65028
1997
Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations. Zbl 1174.65382
Deng, Yuan-Bei; Bai, Zhong-Zhi; Gao, Yong-Hua
2006
Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations. Zbl 1363.65049
Hezari, Davod; Edalatpour, Vahid; Khojasteh Salkuyeh, Davod
2015
A splitting preconditioner for saddle point problems. Zbl 1249.65065
Cao, Yang; Jiang, Mei-Qun; Zheng, Ying-Long
2011
Harmonic projection methods for large non-symmetric eigenvalue problems. Zbl 0937.65045
Morgan, R. B.; Zeng, M.
1998
Convergence analysis of a block improvement method for polynomial optimization over unit spheres. Zbl 1374.65105
Wang, Yiju; Caccetta, Louis; Zhou, Guanglu
2015
A new investigation of the extended Krylov subspace method for matrix function evaluations. Zbl 1240.65154
Knizhnerman, L.; Simoncini, V.
2010
Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models. Zbl 1289.65048
Bai, Zhong-Zhi
2012
Efficient preconditioning scheme for block partitioned matrices with structured sparsity. Zbl 1051.65059
Poirier, Bill
2000
ARMS: an algebraic recursive multilevel solver for general sparse linear systems. Zbl 1071.65001
2002
Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations. Zbl 1174.65381
Bai, Zhong-Zhi; Guo, Xiao-Xia; Xu, Shu-Fang
2006
Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations. Zbl 1212.65175
Damm, T.
2008
Existence of a low rank or $$\mathcal H$$-matrix approximant to the solution of a Sylvester equation. Zbl 1164.65381
Grasedyck, L.
2004
Preconditioners for the discretized time-harmonic Maxwell equations in mixed form. Zbl 1199.78010
Greif, Chen; Schötzau, Dominik
2007
Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor. Zbl 1274.65129
Zhang, Liping; Qi, Liqun
2012
Indefinitely preconditioned inexact Newton method for large sparse equality constrained nonlinear programming problems. Zbl 0937.65066
1998
Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems. Zbl 1199.65109
Li, Liang; Huang, Ting-Zhu; Liu, Xing-Ping
2007
Tridiagonal Toeplitz matrices: properties and novel applications. Zbl 1289.65082
Noschese, Silvia; Pasquini, Lionello; Reichel, Lothar
2013
Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations. Zbl 1349.65104
Lu, Xin; Pang, Hong-Kui; Sun, Hai-Wei
2015
Block-triangular preconditioners for PDE-constrained optimization. Zbl 1240.65097
Rees, Tyrone; Stoll, Martin
2010
Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem. Zbl 1071.65516
Notay, Y.
2002
The inverse problem of bisymmetric matrices with a submatrix constraint. Zbl 1164.15322
Peng, Zhen-yun; Hu, Xi-yan; Zhang, Lei
2004
Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations. Zbl 1463.65040
Bai, Zhong-Zhi; Lu, Kang-Ya; Pan, Jian-Yu
2017
Augmentation block preconditioners for saddle point-type matrices with singular $$(1,1)$$ blocks. Zbl 1212.65146
Cao, Zhi-Hao
2008
High quality preconditioning of a general symmetric positive definite matrix based on its $$U^T U + U^T R + R^T U$$-decomposition. Zbl 0969.65037
Kaporin, I. E.
1998
Eigenvalue estimates for preconditioned saddle point matrices. Zbl 1224.65080
Axelsson, Owe; Neytcheva, Maya
2006
A Power-Arnoldi algorithm for computing PageRank. Zbl 1199.65125
Wu, Gang; Wei, Yimin
2007
On two-grid convergence estimates. Zbl 1164.65343
Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T.
2005
Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Zbl 1224.65263
Dobrev, Veselin A.; Lazarov, Raytcho D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T.
2006
On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations. Zbl 1413.65128
Beik, Fatemeh Panjeh Ali; Saberi Movahed, Farid; Ahmadi-Asl, Salman
2016
A simpler GMRES. Zbl 0838.65030
Walker, Homer F.; Zhou, Lu
1994
Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism. Zbl 1051.65050
Carpentieri, B.; Duff, I. S.; Giraud, L.
2000
The modulus-based matrix splitting algorithms for a class of weakly nonlinear complementarity problems. Zbl 1413.65253
Huang, Na; Ma, Changfeng
2016
Efficient estimation of eigenvalue counts in an interval. Zbl 1413.65092
Di Napoli, Edoardo; Polizzi, Eric; Saad, Yousef
2016
Displacement decomposition – incomplete factorization preconditioning techniques for linear elasticity problems. Zbl 0837.65021
1994
Diagonally compensated reduction and related preconditioning methods. Zbl 0837.65023
Axelsson, O.; Kolotilina, L.
1994
Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems. Zbl 1274.65313
Bastian, Peter; Blatt, Markus; Scheichl, Robert
2012
A survey of spectral factorization methods. Zbl 1053.47013
Sayed, A. H.; Kailath, T.
2001
Several variants of the Hermitian and skew-Hermitian splitting method for a class of complex symmetric linear systems. Zbl 1363.65055
Wu, Shi-Liang
2015
A finite volume element method for a non-linear elliptic problem. Zbl 1164.65494
Chatzipantelidis, P.; Ginting, V.; Lazarov, R. D.
2005
A note on the representation and definition of semiseparable matrices. Zbl 1164.15341
Vandebril, Raf; Van Barel, Marc; Mastronardi, Nicola
2005
On the convergence of shifted Laplace preconditioner combined with multilevel deflation. Zbl 1313.65293
Sheikh, A. H.; Lahaye, D.; Vuik, C.
2013
New convergence results and preconditioning strategies for the conjugate gradient method. Zbl 0837.65027
Kaporin, I. E.
1994
On the convergence of general stationary iterative methods for range-Hermitian singular linear systems. Zbl 1240.65120
Zhang, Naimin; Wei, Yi-Min
2010
Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic. Zbl 0831.65042
1995
Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs. Zbl 1265.65256
MacLachlan, Scott P.; Oosterlee, C. W.
2011
A probing method for computing the diagonal of a matrix inverse. Zbl 1274.65132
2012
Decoupling preconditioners in the implicit parallel accurate reservoir simulator (IPARS). Zbl 1071.76583
Lacroix, Sébastien; Vassilevski, Yuri V.; Wheeler, Mary F.
2001
On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling. Zbl 0840.65021
Freund, Roland W.; Hochbruck, Marlis
1994
Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form. Zbl 1224.65099
Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker
2009
Recursive Krylov-based multigrid cycles. Zbl 1212.65132
Notay, Y.; Vassilevski, P. S.
2008
A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test. Zbl 1438.65060
Chen, Haibin; Chen, Yannan; Li, Guoyin; Qi, Liqun
2018
A fast algorithm for the spectral radii of weakly reducible nonnegative tensors. Zbl 06861606
Zhou, Guanglu; Wang, Gang; Qi, Liqun; Alqahtani, Mohammed
2018
An algebraic multigrid method for finite element discretizations with edge elements. Zbl 1071.65170
Reitzinger, S.; Schöberl, J.
2002
Local Fourier analysis of the complex shifted Laplacian preconditioner for Helmholtz problems. Zbl 1313.65320
Cools, Siegfried; Vanroose, Wim
2013
More on extremal ranks of the matrix expressions $$A-BX \pm X^{*}B^{*}$$ with statistical applications. Zbl 1212.15029
Liu, Y.; Tian, Y.
2008
A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations. Zbl 0983.65107
Gander, Martin J.
1999
Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems. Zbl 1071.65512
Durazzi, C.; Ruggiero, V.
2003
Efficient approximation of random fields for numerical applications. Zbl 1349.65048
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
2015
A spectral algorithm for envelope reduction of sparse matrices. Zbl 0833.65038
Barnard, Stephen T.; Pothen, Alex; Simon, Horst
1995
On greedy randomized coordinate descent methods for solving large linear least-squares problems. Zbl 1449.65128
Bai, Zhong-Zhi; Wu, Wen-Ting
2019
Fast Hankel tensor-vector product and its application to exponential data fitting. Zbl 1349.65070
Ding, Weiyang; Qi, Liqun; Wei, Yimin
2015
On SSOR-like preconditioners for non-Hermitian positive definite matrices. Zbl 1413.65040
Bai, Zhong-Zhi
2016
Distance-two interpolation for parallel algebraic multigrid. Zbl 1212.65139
Sterck, Hans De; Falgout, Robert D.; Nolting, Joshua W.; Yang, Ulrike Meier
2008
Algebraic multilevel preconditioning of finite element matrices using local Schur complements. Zbl 1174.65398
Kraus, J. K.
2006
A robust incomplete factorization preconditioner for positive definite matrices. Zbl 1071.65528
Benzi, Michele; Tůma, Miroslav
2003
Stability of block. Zbl 0834.65010
Demmel, James W.; Higham, Nicholas J.; Schreiber, Robert S.
1995
Trace optimization and eigenproblems in dimension reduction methods. Zbl 1249.65075
Kokiopoulou, E.; Chen, Jie; Saad, Yousef
2011
A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart. Zbl 1114.65112
Murillo, Maria; Cai, Xiao-Chuan.
2004
Splitting methods for tensor equations. Zbl 1463.65049
Li, Dong-Hui; Xie, Shuilian; Xu, Hong-Ru
2017
On the performance of various adaptive preconditioned GMRES strategies. Zbl 0937.65036
Burrage, K.; Erhel, J.
1998
Asymptotic convergence of conjugate gradient methods for the partial symmetric eigenproblem. Zbl 0889.65032
Bergamaschi, L.; Gambolati, G.; Pini, G.
1997
Exponential data fitting using multilinear algebra: The single-channel and multi-channel case. Zbl 1164.93012
Papy, J. M.; De Lathauwer, L.; Van Huffel, S.
2005
Multigrid methods for the symmetric interior penalty method on graded meshes. Zbl 1224.65288
Brenner, S. C.; Cui, J.; Sung, L.-Y.
2009
An approximate BDDC preconditioner. Zbl 1199.65088
Dohrmann, C. R.
2007
On eigenvalue distribution of constraint-preconditioned symmetric saddle point matrices. Zbl 1274.65084
Bergamaschi, Luca
2012
Optimal solvers for linear systems with fractional powers of sparse SPD matrices. Zbl 06986996
Harizanov, S.; Lazarov, R.; Margenov, S.; Marinov, P.; Vutov, Y.
2018
Accelerated derivative-free method for nonlinear monotone equations with an application. Zbl 07511605
Ibrahim, Abdulkarim Hassan; Kumam, Poom; Abubakar, Auwal Bala; Adamu, Abubakar
2022
Block low-rank single precision coarse grid solvers for extreme scale multigrid methods. Zbl 07511588
Buttari, Alfredo; Huber, Markus; Leleux, Philippe; Mary, Theo; Rüde, Ulrich; Wohlmuth, Barbara
2022
The tensor Golub-Kahan-Tikhonov method applied to the solution of ill-posed problems with a t-product structure. Zbl 07511593
Reichel, Lothar; Ugwu, Ugochukwu O.
2022
Computation of generalized inverses of tensors via $$t$$-product. Zbl 07511597
Behera, Ratikanta; Sahoo, Jajati Keshari; Mohapatra, Ram N.; Nashed, M. Zuhair
2022
Fast iterative solver for the optimal control of time-dependent PDEs with Crank-Nicolson discretization in time. Zbl 07511600
Leveque, Santolo; Pearson, John W.
2022
Mixed precision $$s$$-step Lanczos and conjugate gradient algorithms. Zbl 07511606
Carson, Erin; Gergelits, Tomáš; Yamazaki, Ichitaro
2022
A local Fourier analysis of additive Vanka relaxation for the Stokes equations. Zbl 07361104
Farrell, Patrick E.; He, Yunhui; MacLachlan, Scott P.
2021
Low synchronization Gram-Schmidt and generalized minimal residual algorithms. Zbl 1474.65103
Świrydowicz, Katarzyna; Langou, Julien; Ananthan, Shreyas; Yang, Ulrike; Thomas, Stephen
2021
Bounds on the spectra of Schur complements of large H-TFETI-DP clusters for 2D Laplacian. Zbl 07332757
Dostál, Zdeněk; Horák, David; Brzobohatý, Tomáš; Vodstrčil, Petr
2021
A novel direct method based on the Lucas multiwavelet functions for variable-order fractional reaction-diffusion and subdiffusion equations. Zbl 07332759
Dehestani, Haniye; Ordokhani, Yadollah; Razzaghi, Mohsen
2021
Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection. Zbl 07396250
De Sterck, Hans; Falgout, Robert D.; Friedhoff, Stephanie; Krzysik, Oliver A.; MacLachlan, Scott P.
2021
Semiconvergence analysis of the randomized row iterative method and its extended variants. Zbl 1474.65102
Wu, Nianci; Xiang, Hua
2021
Gratton, Serge; Simon, Ehouarn; Titley-Peloquin, David; Toint, Philippe L.
2021
On “optimal” $$h$$-independent convergence of Parareal and multigrid-reduction-in-time using Runge-Kutta time integration. Zbl 07361111
Friedhoff, Stephanie; Southworth, Ben S.
2021
Oviedo, Harry; Dalmau, Oscar; Herrera, Rafael
2021
Cell-by-cell approximate Schur complement technique in preconditioning of meshfree discretized piezoelectric equations. Zbl 07396245
Cao, Yang; Neytcheva, Maya
2021
Condition numbers for the truncated total least squares problem and their estimations. Zbl 07478602
Meng, Qing-Le; Diao, Huai-An; Bai, Zheng-Jian
2021
All-at-once solution of linear wave equations. Zbl 07478618
Danieli, Federico; Wathen, Andrew J.
2021
Asymptotic spectra of large matrices coming from the symmetrization of Toeplitz structure functions and applications to preconditioning. Zbl 07332746
Ferrari, Paola; Barakitis, Nikos; Serra-Capizzano, Stefano
2021
On the numerical solution of ill-conditioned linear systems by regularization and iteration. Zbl 07332749
Spigler, Renato
2021
A method for computing the Perron root for primitive matrices. Zbl 07332754
Dembélé, Doulaye
2021
Matrix-free preconditioning for high-order $$H$$(curl) discretizations. Zbl 07332761
Barker, Andrew T.; Kolev, Tzanio
2021
Preconditioning Navier-Stokes control using multilevel sequentially semiseparable matrix computations. Zbl 07332762
Qiu, Yue; van Gijzen, Martin B.; van Wingerden, Jan-Willem; Verhaegen, Michel; Vuik, Cornelis
2021
Multilevel graph embedding. Zbl 07361105
Quiring, Benjamin; Vassilevski, Panayot S.
2021
Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications. Zbl 07396240
Donatelli, Marco; Ferrari, Paola; Furci, Isabella; Serra-Capizzano, Stefano; Sesana, Debora
2021
A gradient-type iterative method for impulse noise removal. Zbl 07396242
Liu, Jinkui; Cao, Haisong; Zhao, Yongxiang; Zhang, Liqiao
2021
A new preconditioning approach for an interior point-proximal method of multipliers for linear and convex quadratic programming. Zbl 07396244
Bergamaschi, Luca; Gondzio, Jacek; Martínez, Ángeles; Pearson, John W.; Pougkakiotis, Spyridon
2021
A fast spectral divide-and-conquer method for banded matrices. Zbl 07396248
Šušnjara, Ana; Kressner, Daniel
2021
A derivative-free scaling memoryless Broyden-Fletcher-Goldfarb-Shanno method for solving a system of monotone nonlinear equations. Zbl 07478606
Ullah, Najib; Sabi&rsquo;u, Jamilu; Shah, Abdullah
2021
Incomplete inverse matrices. Zbl 07478611
2021
An efficient algorithm for solving the nonnegative tensor least squares problem. Zbl 07478617
Duan, Xue-Feng; Duan, Shan-Qi; Li, Juan; Li, Jiao-fen; Wang, Qing-Wen
2021
Nonoverlapping block smoothers for the Stokes equations. Zbl 07478621
Claus, Lisa; Bolten, Matthias
2021
ODE-based double-preconditioning for solving linear systems $$A^{\alpha}x=b$$ and $$f(A)x=b$$. Zbl 07478625
Antoine, Xavier; Lorin, Emmanuel
2021
Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems. Zbl 07478628
Baghel, Mohit Kumar; Gillis, Nicolas; Sharma, Punit
2021
Robust tensor completion using transformed tensor singular value decomposition. Zbl 07217207
Song, Guangjing; Ng, Michael K.; Zhang, Xiongjun
2020
Approximation of a fractional power of an elliptic operator. Zbl 1474.65482
Vabishchevich, P. N.
2020
Non-Hermitian perturbations of Hermitian matrix-sequences and applications to the spectral analysis of the numerical approximation of partial differential equations. Zbl 1474.65454
Barbarino, Giovanni; Serra-Capizzano, Stefano
2020
Convergence analysis for parallel-in-time solution of hyperbolic systems. Zbl 1463.65280
De Sterck, Hans; Friedhoff, Stephanie; Howse, Alexander J. M.; MacLachlan, Scott P.
2020
Interior-point methods and preconditioning for PDE-constrained optimization problems involving sparsity terms. Zbl 07177902
Pearson, John W.; Porcelli, Margherita; Stoll, Martin
2020
Two-level Fourier analysis of multigrid for higher-order finite-element discretizations of the Laplacian. Zbl 1463.65403
He, Yunhui; MacLachlan, Scott
2020
Nesterov acceleration of alternating least squares for canonical tensor decomposition: momentum step size selection and restart mechanisms. Zbl 1488.65108
Mitchell, Drew; Ye, Nan; De Sterck, Hans
2020
Modulus-based synchronous multisplitting methods for solving horizontal linear complementarity problems on parallel computers. Zbl 07286030
2020
Extrapolation methods for fixed-point multilinear PageRank computations. Zbl 1488.65106
Cipolla, Stefano; Redivo-Zaglia, Michela; Tudisco, Francesco
2020
The tensor t-function: a definition for functions of third-order tensors. Zbl 1463.15052
Lund, Kathryn
2020
Further results on the Drazin inverse of even-order tensors. Zbl 1474.15063
Behera, Ratikanta; Nandi, Ashish Kumar; Sahoo, Jajati Keshari
2020
Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory. Zbl 1463.65087
Angelova, V.; Hached, M.; Jbilou, K.
2020
Preconditioned tensor splitting AOR iterative methods for $$\mathcal{H}$$-tensor equations. Zbl 1488.65109
Wang, Xuezhong; Che, Maolin; Wei, Yimin
2020
On regularized Hermitian splitting iteration methods for solving discretized almost-isotropic spatial fractional diffusion equations. Zbl 1463.65039
Bai, Zhong-Zhi; Lu, Kang-Ya
2020
Right preconditioned MINRES for singular systems. Zbl 1463.65058
Sugihara, Kota; Hayami, Ken; Zheng, Ning
2020
A locally and cubically convergent algorithm for computing $$\mathcal{Z}$$-eigenpairs of symmetric tensors. Zbl 1474.65091
Zhao, Ruijuan; Zheng, Bing; Liang, Maolin; Xu, Yangyang
2020
On approximating the nearest $$\Omega$$-stable matrix. Zbl 07217198
Choudhary, Neelam; Gillis, Nicolas; Sharma, Punit
2020
Decompositions of third-order tensors: HOSVD, T-SVD, and Beyond. Zbl 07217200
Zeng, Chao; Ng, Michael K.
2020
Accurate bidiagonal decomposition of collocation matrices of weighted $$\varphi$$-transformed systems. Zbl 07217202
Mainar, Esmeralda; Peña, Juan Manuel; Rubio, Beatriz
2020
Effectiveness and robustness revisited for a preconditioning technique based on structured incomplete factorization. Zbl 07217203
Xin, Zixing; Xia, Jianlin; Cauley, Stephen; Balakrishnan, Venkataramanan
2020
Numerical study in stochastic homogenization for elliptic partial differential equations: convergence rate in the size of representative volume elements. Zbl 07217205
Khoromskaia, Venera; Khoromskij, Boris N.; Otto, Felix
2020
Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems. Zbl 07250714
Campos, Carmen; Roman, Jose E.
2020
Parameter estimation in the Hermitian and skew-Hermitian splitting method using gradient iterations. Zbl 1474.65082
Zou, Qinmeng; Magoulès, Frédéric
2020
Computing the matrix geometric mean: Riemannian versus Euclidean conditioning, implementation techniques, and a Riemannian BFGS method. Zbl 1474.65131
Yuan, Xinru; Huang, Wen; Absil, P.-A.; Gallivan, Kyle A.
2020
NURBS in isogeometric discretization methods: a spectral analysis. Zbl 1474.35263
Garoni, Carlo; Manni, Carla; Serra-Capizzano, Stefano; Speleers, Hendrik
2020
An extension of the Cayley transform method for a parameterized generalized inverse eigenvalue problem. Zbl 1474.65092
Dalvand, Zeynab; Hajarian, Masoud; Roman, Jose E.
2020
Stably computing the multiplicity of known roots given leading coefficients. Zbl 07177901
Clark, Gregory J.; Cooper, Joshua N.
2020
Structured FISTA for image restoration. Zbl 1488.65084
Chen, Zixuan; Nagy, James G.; Xi, Yuanzhe; Yu, Bo
2020
Synchronous and asynchronous optimized Schwarz methods for one-way subdivision of bounded domains. Zbl 07177904
2020
A two-grid method for characteristic expanded mixed finite element solution of miscible displacement problem. Zbl 07217201
Hu, Hanzhang; Chen, Yanping
2020
Semi-active $$\mathcal{H}_{\infty}$$ damping optimization by adaptive interpolation. Zbl 1463.93076
Tomljanović, Zoran; Voigt, Matthias
2020
Spectral analysis of $$\mathbb{P}_k$$ finite element matrices in the case of Friedrichs-Keller triangulations via generalized locally Toeplitz technology. Zbl 07250717
Rahla, Ryma Imene; Serra-Capizzano, Stefano; Tablino-Possio, Cristina
2020
Multicolor low-rank preconditioner for general sparse linear systems. Zbl 1474.65070
Zheng, Qingqing; Xi, Yuanzhe; Saad, Yousef
2020
On inexact alternating direction implicit iteration for continuous Sylvester equations. Zbl 1474.65112
Liu, Zhongyun; Zhou, Yang; Zhang, Yulin
2020
Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems. Zbl 07286028
Saibaba, Arvind K.; Chung, Julianne; Petroske, Katrina
2020
Compact quasi-Newton preconditioners for symmetric positive definite linear systems. Zbl 1488.65063
Bergamaschi, Luca; Marín, José; Martínez, Ángeles
2020
On greedy randomized coordinate descent methods for solving large linear least-squares problems. Zbl 1449.65128
Bai, Zhong-Zhi; Wu, Wen-Ting
2019
Tight upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithms. Zbl 07088859
Du, Kui
2019
Conservative discretizations and parameter-robust preconditioners for Biot and multiple-network flux-based poroelasticity models. Zbl 1463.65372
Hong, Qingguo; Kraus, Johannes; Lymbery, Maria; Philo, Fadi
2019
Robust quaternion matrix completion with applications to image inpainting. Zbl 1474.65126
Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing
2019
Krylov subspace methods to solve a class of tensor equations via the Einstein product. Zbl 1463.65045
Huang, Baohua; Xie, Yajun; Ma, Changfeng
2019
Randomized algorithms for total least squares problems. Zbl 07031719
Xie, Pengpeng; Xiang, Hua; Wei, Yimin
2019
On the applicability of Genocchi wavelet method for different kinds of fractional-order differential equations with delay. Zbl 1463.65204
Dehestani, Haniye; Ordokhani, Yadollah; Razzaghi, Mohsen
2019
Direct and iterative methods for interval parametric algebraic systems producing parametric solutions. Zbl 1463.65108
2019
On the singular Neumann problem in linear elasticity. Zbl 07031712
Kuchta, Miroslav; Mardal, Kent-Andre; Mortensen, Mikael
2019
Accurate computations with Laguerre matrices. Zbl 07031717
Delgado, Jorge; Orera, Héctor; Peña, Juan Manuel
2019
Perturbation analysis for mixed least squares-total least squares problems. Zbl 1474.65098
Zheng, Bing; Yang, Zhanshan
2019
A comparison of preconditioned Krylov subspace methods for large-scale nonsymmetric linear systems. Zbl 07031715
Ghai, Aditi; Lu, Cao; Jiao, Xiangmin
2019
Relaxation methods for solving the tensor equation arising from the higher-order Markov chains. Zbl 07144925
Liu, Dongdong; Li, Wen; Vong, Seak-Weng
2019
Uzawa methods for a class of block three-by-three saddle-point problems. Zbl 1463.65046
Huang, Na; Dai, Yu-Hong; Hu, QiYa
2019
Hybrid enriched bidiagonalization for discrete ill-posed problems. Zbl 1449.65093
Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi
2019
Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices. Zbl 1449.15071
Noschese, Silvia; Reichel, Lothar
2019
Preconditioning for boundary control problems in incompressible fluid dynamics. Zbl 07031718
2019
A parallel time integrator for solving the linearized shallow water equations on the rotating sphere. Zbl 07031721
Schreiber, Martin; Loft, Richard
2019
On the distribution of real eigenvalues in linear viscoelastic oscillators. Zbl 07031728
2019
Nonsingular systems of generalized Sylvester equations: an algorithmic approach. Zbl 1474.65108
De Terán, Fernando; Iannazzo, Bruno; Poloni, Federico; Robol, Leonardo
2019
Direct solution method for the equilibrium problem for elastic stents. Zbl 1449.74125
Grubišić, Luka; Tambača, Josip
2019
Spectral condition-number estimation of large sparse matrices. Zbl 1449.65097
Avron, Haim; Druinsky, Alex; Toledo, Sivan
2019
A coarse-fine-mesh stabilization for an alternating Schwarz domain decomposition method. Zbl 1463.65400
Axelsson, Owe; Gustafsson, Ivar
2019
Subspace methods for three-parameter eigenvalue problems. Zbl 1463.65071
Hochstenbach, Michiel E.; Meerbergen, Karl; Mengi, Emre; Plestenjak, Bor
2019
Accelerating the iterative solution of convection-diffusion problems using singular value decomposition. Zbl 1463.65075
Pitton, Giuseppe; Heltai, Luca
2019
A restarted Krylov method with inexact inversions. Zbl 07031713
Dax, Achiya
2019
A compact rational Krylov method for large-scale rational eigenvalue problems. Zbl 07031714
Dopico, Froilán M.; González-Pizarro, Javier
2019
A Riemannian variant of the Fletcher-Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata. Zbl 07031722
Yao, Teng-Teng; Bai, Zheng-Jian; Zhao, Zhi
2019
A primal-dual method for the Meyer model of cartoon and texture decomposition. Zbl 07031724
Wen, You-Wei; Sun, Hai-Wei; Ng, Michael K.
2019
Regularizing properties of a class of matrices including the optimal and the superoptimal preconditioners. Zbl 07031725
Cipolla, Stefano; Di Fiore, Carmine; Durastante, Fabio; Zellini, Paolo
2019
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### Cited by 7,326 Authors

 114 Wei, Yimin 91 Ma, Changfeng 88 Huang, Ting-Zhu 74 Qi, Liqun 63 Reichel, Lothar 61 Zhang, Guofeng 59 Benner, Peter 58 Axelsson, Axel Owe Holger 47 Serra-Capizzano, Stefano 44 Simoncini, Valeria 41 Li, Wen 40 Ng, Michael Kwok-Po 40 Wu, Shiliang 38 Li, Chaoqian 36 Bai, Zhongzhi 36 Liang, Zhaozheng 35 Chen, Guoliang 35 Li, Yaotang 34 Li, Cuixia 32 Huang, Zhengge 32 Vuik, Cornelis 31 Jia, Zhongxiao 31 Khojasteh Salkuyeh, Davod 30 Cao, Yang 30 Saad, Yousef 30 Zheng, Bing 29 Cui, Jingjing 29 Li, Zi-Cai 29 Vassilevski, Panayot Spirov 29 Wang, Qingwen 28 Hu, Xiaozhe 28 Szyld, Daniel B. 27 Benzi, Michele 27 Gu, Xian-Ming 27 Hajarian, Masoud 27 Vandebril, Raf 27 Yang, Aili 26 Gaspar, Francisco José 26 Van Barel, Marc 26 Vong, Seakweng 26 Wu, Yujiang 25 Donatelli, Marco 25 Dostál, Zdeněk 25 Gander, Martin Jakob 25 Margenov, Svetozar D. 25 Neytcheva, Maya G. 25 Rodrigo, Carmen 25 Zheng, Hua 24 Ferronato, Massimiliano 24 Jbilou, Khalide 24 Lin, Wen-Wei 24 Wang, Xiang 23 Chen, Haibin 23 Klawonn, Axel 23 Wang, Yiju 23 Xu, Jinchao 23 Yin, Junfeng 23 Zikatanov, Ludmil T. 22 Bergamaschi, Luca 22 Dai, Hua 22 Ke, Yifen 22 Kressner, Daniel 22 Peña, Juan Manuel 21 Blaheta, Radim 21 Carpentieri, Bruno 21 Huang, Hung-Tsai 21 Huang, Na 21 Pavarino, Luca Franco 21 Stoll, Martin 21 Zhao, Xile 20 Diao, Huaian 20 Khoromskiĭ, Boris Nikolaevich 20 Mehrmann, Volker 20 Wu, Gang 19 Brenner, Susanne Cecelia 19 Gemignani, Luca 19 He, Jun 19 Kraus, Johannes K. 19 Lu, Linzhang 19 MacLachlan, Scott P. 19 Notay, Yvan 19 Rheinbach, Oliver 19 Tian, Yongge 19 Xia, Jianlin 19 Xu, Zhong 19 Zhao, Jianxing 18 Argyros, Ioannis Konstantinos 18 Bini, Dario Andrea 18 Gu, Chuanqing 18 Harbrecht, Helmut 18 Kürschner, Patrick 18 Mardal, Kent-Andre 18 Niu, Qiang 18 Wu, Shulin 18 Zhou, Guanglu 17 Chen, Fang 17 Chen, Ke 17 Elman, Howard C. 17 Janna, Carlo 17 Li, Hanyu ...and 7,226 more Authors
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### Cited in 481 Journals

 547 Journal of Computational and Applied Mathematics 427 Linear Algebra and its Applications 382 SIAM Journal on Scientific Computing 322 Applied Mathematics and Computation 306 Numerical Algorithms 296 Numerical Linear Algebra with Applications 265 Computers & Mathematics with Applications 253 Journal of Computational Physics 199 Computer Methods in Applied Mechanics and Engineering 191 Applied Numerical Mathematics 167 SIAM Journal on Matrix Analysis and Applications 149 Journal of Scientific Computing 124 Computational and Applied Mathematics 119 Numerische Mathematik 116 BIT 99 International Journal of Computer Mathematics 87 Linear and Multilinear Algebra 81 Applied Mathematics Letters 71 Calcolo 66 Mathematics of Computation 63 East Asian Journal on Applied Mathematics 57 Advances in Computational Mathematics 54 International Journal for Numerical Methods in Engineering 54 Mathematics and Computers in Simulation 54 Computational Optimization and Applications 51 ETNA. Electronic Transactions on Numerical Analysis 48 SIAM Journal on Numerical Analysis 47 Journal of Inequalities and Applications 45 Journal of Applied Mathematics and Computing 43 Mathematical Problems in Engineering 42 Journal of Optimization Theory and Applications 38 Engineering Analysis with Boundary Elements 36 Computers and Fluids 36 Journal of Applied Mathematics 34 Frontiers of Mathematics in China 32 Computational Geosciences 32 Computational Methods in Applied Mathematics 30 Computing 30 Applied Mathematical Modelling 29 Journal of Mathematical Analysis and Applications 28 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 27 Journal of Industrial and Management Optimization 26 Automatica 26 Japan Journal of Industrial and Applied Mathematics 26 Journal of Numerical Mathematics 25 Filomat 24 Numerical Methods for Partial Differential Equations 24 Computing and Visualization in Science 24 Optimization Methods & Software 24 Communications in Computational Physics 23 Computational Mechanics 23 Abstract and Applied Analysis 22 Applications of Mathematics 21 ELA. The Electronic Journal of Linear Algebra 21 Advances in Applied Mathematics and Mechanics 20 Inverse Problems 20 Science China. Mathematics 20 SIAM/ASA Journal on Uncertainty Quantification 19 Journal of the Franklin Institute 18 Journal of Mathematical Sciences (New York) 17 Multiscale Modeling & Simulation 16 International Journal for Numerical Methods in Fluids 16 Numerical Functional Analysis and Optimization 16 Systems & Control Letters 15 Archives of Computational Methods in Engineering 15 Open Mathematics 14 Computer Physics Communications 14 Journal of Global Optimization 14 SIAM Review 14 AIMS Mathematics 13 Mathematical and Computer Modelling 13 Mediterranean Journal of Mathematics 13 Numerical Algebra, Control and Optimization 13 Communications on Applied Mathematics and Computation 12 Journal of Applied Analysis and Computation 11 Acta Numerica 11 SIAM Journal on Imaging Sciences 11 Results in Applied Mathematics 10 International Journal of Control 10 Bulletin of the Iranian Mathematical Society 10 Computational Mathematics and Mathematical Physics 10 European Journal of Operational Research 10 Applied and Computational Harmonic Analysis 10 Advances in Applied Clifford Algebras 9 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 9 Mathematical Programming. Series A. Series B 9 SIAM Journal on Optimization 9 Communications in Numerical Methods in Engineering 9 SIAM Journal on Applied Dynamical Systems 9 GAMM-Mitteilungen 9 Optimization Letters 9 S$$\vec{\text{e}}$$MA Journal 9 Special Matrices 8 ACM Transactions on Mathematical Software 8 Computer Aided Geometric Design 8 Journal of Mathematical Imaging and Vision 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 8 International Journal of Computational Methods 8 Inverse Problems in Science and Engineering 8 Journal of the Operations Research Society of China ...and 381 more Journals
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### Cited in 59 Fields

 5,570 Numerical analysis (65-XX) 1,804 Linear and multilinear algebra; matrix theory (15-XX) 1,038 Partial differential equations (35-XX) 635 Fluid mechanics (76-XX) 574 Operations research, mathematical programming (90-XX) 396 Mechanics of deformable solids (74-XX) 279 Systems theory; control (93-XX) 270 Calculus of variations and optimal control; optimization (49-XX) 254 Computer science (68-XX) 179 Operator theory (47-XX) 179 Probability theory and stochastic processes (60-XX) 156 Optics, electromagnetic theory (78-XX) 150 Information and communication theory, circuits (94-XX) 143 Statistics (62-XX) 122 Combinatorics (05-XX) 115 Ordinary differential equations (34-XX) 104 Biology and other natural sciences (92-XX) 68 Approximations and expansions (41-XX) 66 Statistical mechanics, structure of matter (82-XX) 61 Quantum theory (81-XX) 60 Geophysics (86-XX) 59 Dynamical systems and ergodic theory (37-XX) 49 Real functions (26-XX) 46 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 43 Integral equations (45-XX) 36 Harmonic analysis on Euclidean spaces (42-XX) 33 Mechanics of particles and systems (70-XX) 32 Functional analysis (46-XX) 27 Differential geometry (53-XX) 24 Classical thermodynamics, heat transfer (80-XX) 22 Special functions (33-XX) 21 Number theory (11-XX) 17 Functions of a complex variable (30-XX) 15 Field theory and polynomials (12-XX) 14 General and overarching topics; collections (00-XX) 14 Difference and functional equations (39-XX) 11 History and biography (01-XX) 11 Algebraic geometry (14-XX) 10 Integral transforms, operational calculus (44-XX) 10 Global analysis, analysis on manifolds (58-XX) 9 Commutative algebra (13-XX) 8 Potential theory (31-XX) 6 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Astronomy and astrophysics (85-XX) 3 Nonassociative rings and algebras (17-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 3 Convex and discrete geometry (52-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 2 Relativity and gravitational theory (83-XX) 1 Topological groups, Lie groups (22-XX) 1 General topology (54-XX)