## Golub, Gene Howard

Compute Distance To:
 Author ID: golub.gene-h Published as: Golub, Gene H.; Golub, G. H.; Golub, Gene; Golub, G. External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef
 Documents Indexed: 257 Publications since 1961, including 14 Books 9 Contributions as Editor Biographic References: 5 Publications Co-Authors: 185 Co-Authors with 243 Joint Publications 5,517 Co-Co-Authors
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### Co-Authors

 18 single-authored 10 Van Loan, Charles Francis 9 Boley, Daniel L. 8 Bai, Zhongzhi 8 Concus, Paul 8 O’Leary, Dianne P. 7 Gander, Walter 7 Meurant, Gérard A. 7 Milanfar, Peyman 6 Calvetti, Daniela 6 Elhay, Sylvan 6 Elman, Howard C. 6 Reichel, Lothar 5 Chan, Tony Fan-Cheong 5 Chu, Moody T. 5 Greif, Chen 5 Kautsky, Jaroslav 5 Law, Kincho H. 5 Plemmons, Robert James 5 Van Dooren, Paul M. 5 von Matt, Urs 5 Zha, Hongyuan 4 Arbenz, Peter 4 Bartels, Richard Harold 4 Benzi, Michele 4 Ortega, James M. 4 Van Barel, Marc 4 Vandebril, Raf 4 Varah, James M. 4 Yuan, Jinyun 4 Zhang, Tong 3 Bai, Zhaojun 3 Bertaccini, Daniele 3 Chandrasekaran, Shivkumar 3 Fischer, Bernd 3 Funderlic, Robert E. 3 Gu, Ming 3 Hansen, Per Christian 3 LeVeque, Randall J. 3 Luk, Franklin T. 3 Nash, Stephen G. 3 Ng, Michael Kwok-Po 3 Overton, Michael L. 3 Saunders, Michael A. 3 Sayed, Ali H. 3 Serra-Capizzano, Stefano 3 Strebel, Rolf 3 Van der Vorst, Henk Albertus 3 Wathen, Andrew John 3 Wilkinson, James Hardy 3 Ye, Qiang 2 Berry, Michael W. 2 Björck, Åke 2 Buzbee, Billy L. 2 Chan, Raymond Hon-Fu 2 Chang, Xiaowen 2 Cuyt, Annie A. M. 2 Dahlquist, Germund 2 de Boor, Carl 2 De Moor, Bart L. R. 2 Elad, Michael 2 Fierro, Ricardo D. 2 Gautschi, Walter 2 Greenbaum, Anne 2 Gutknecht, Martin H. 2 Hald, Ole Hansen 2 Kågström, Bo 2 Lee, Chris P. 2 Li, Chi-Kwong 2 Liao, Li-Zhi 2 Mastronardi, Nicola 2 Mulet, Pep 2 Ram, Yitshak M. 2 Seneta, Eugene 2 Sølna, Knut 2 Stewart, Gilbert Wright 2 Tang, Wei-Pai 2 Underwood, Richard 2 Varga, Richard Steven 2 Verdonk, Brigitte M. 2 Widlund, Olof B. 2 Wu, Xiaonan 2 Zenios, Stefanos A. 2 Zhang, Zhenyue 1 Andersson, Lars-Erik 1 Baglama, James 1 Beckermann, Bernhard 1 Björk, Åke 1 Botchev, Mike A. 1 Boutry, Gregory 1 Brent, Richard Peirce 1 Businger, P. A. 1 Carey, Cheryl M. M. 1 Cecilio, W. A. G. 1 Chu, Delin 1 Cline, Alan K. 1 Comon, Pierre 1 Cottle, Richard W. 1 Cuminato, José Alberto 1 Dorr, Fred W. 1 Drexler, Michael ...and 87 more Co-Authors
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### Serials

 28 SIAM Journal on Matrix Analysis and Applications 16 BIT 15 Numerische Mathematik 15 Linear Algebra and its Applications 14 SIAM Journal on Scientific Computing 13 Mathematics of Computation 11 Numerical Algorithms 8 SIAM Journal on Numerical Analysis 5 Journal of Computational and Applied Mathematics 5 SIAM Review 4 SIAM Journal on Scientific and Statistical Computing 3 Systems & Control Letters 3 Communications of the ACM 3 Numerical Linear Algebra with Applications 2 Bulletin of the Australian Mathematical Society 2 IMA Journal of Numerical Analysis 2 Inverse Problems 2 Calcolo 2 Journal of Econometrics 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 IEEE Transactions on Image Processing 2 Internet Mathematics 2 Acta Numerica 2 Johns Hopkins Series in the Mathematical Sciences 1 The American Statistician 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 ACM Transactions on Mathematical Software 1 Aplikace Matematiky 1 Applied Mathematics and Optimization 1 Computing 1 IEEE Transactions on Automatic Control 1 IEEE Transactions on Computers 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Technometrics 1 SIAM Journal on Algebraic and Discrete Methods 1 Applied Numerical Mathematics 1 IEEE Transactions on Signal Processing 1 IEEE Transactions on Circuits and Systems. II: Analog and Digital Signal Processing 1 Journal of Statistical Computation and Simulation 1 Mitteilungen der Mathematischen Gesellschaft in Hamburg 1 ETNA. Electronic Transactions on Numerical Analysis 1 Annals of Numerical Mathematics 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Berliner Studienreihe zur Mathematik 1 Collection de la Direction des Études et Recherches d’Électricité de France 1 The IMA Volumes in Mathematics and its Applications 1 ISNM. International Series of Numerical Mathematics 1 MAA Studies in Mathematics 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Proceedings of Symposia in Applied Mathematics 1 Texts and Readings in Mathematics 1 Annals of Mathematical Statistics 1 Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis 1 Numerical Mathematics and Scientific Computation 1 Princeton Series in Applied Mathematics
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### Fields

 216 Numerical analysis (65-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 26 Partial differential equations (35-XX) 20 Statistics (62-XX) 18 Computer science (68-XX) 11 General and overarching topics; collections (00-XX) 11 History and biography (01-XX) 9 Operations research, mathematical programming (90-XX) 8 Approximations and expansions (41-XX) 6 Fluid mechanics (76-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 5 Probability theory and stochastic processes (60-XX) 5 Systems theory; control (93-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

235 Publications have been cited 16,759 times in 11,760 Documents Cited by Year
Matrix computations. 3rd ed. Zbl 0865.65009
Golub, Gene; Van Loan, Charles F.
1996
Matrix computations. 2nd ed. Zbl 0733.65016
Golub, Gene H.; Van Loan, Charles F.
1989
Numerical solution of saddle point problems. Zbl 1115.65034
Benzi, Michele; Golub, Gene H.; Liesen, Jörg
2005
Matrix computations. Zbl 0559.65011
Golub, Gene H.; Van Loan, Charles F.
1983
Matrix computations. 4th ed. Zbl 1268.65037
Golub, Gene H.; Van Loan, Charles F.
2013
Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032
Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
2003
Generalized cross-validation as a method for choosing a good ridge parameter. Zbl 0461.62059
Golub, Gene H.; Heath, Michael; Wahba, Grace
1979
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025
Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu
2004
Calculation of Gauss quadrature rules. Zbl 0179.21901
Golub, Gene H.; Welsch, John H.
1969
Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022
Bai, Zhongzhi; Golub, Gene H.
2007
A preconditioner for generalized saddle point problems. Zbl 1082.65034
Benzi, Michele; Golub, Gene H.
2004
A Hessenberg-Schur method for the problem AX+XB=C. Zbl 0421.65022
Golub, Gene H.; Nash, S.; Van Loan, Charles F.
1979
Calculating the singular values and pseudo-inverse of a matrix. Zbl 0194.18201
Golub, G.; Kahan, W.
1965
Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041
Elman, Howard C.; Golub, Gene H.
1994
A note on preconditioning for indefinite linear systems. Zbl 0959.65063
Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J.
2000
On direct methods for solving Poisson’s equations. Zbl 0217.52902
Buzbee, B. L.; Golub, G. H.; Nielson, C. W.
1970
Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028
Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng
2005
A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118
Chan, Tony F.; Golub, Gene H.; Mulet, Pep
1999
The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045
Golub, G. H.; Pereyra, V.
1973
An analysis of the total least squares problem. Zbl 0468.65011
Golub, Gene H.; Van Loan, Charles F.
1980
Some modified matrix eigenvalue problems. Zbl 0254.65027
Golub, Gene H.
1973
SOR-like methods for augmented systems. Zbl 0991.65036
Golub, Gene H.; Wu, X.; Yuan, Jin-Yun
2001
Singular value decomposition and least squares solutions. Zbl 0181.17602
Golub, G. H.; Reinsch, C.
1970
Symmetric tensors and symmetric tensor rank. Zbl 1181.15014
Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard
2008
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2007
Rank-one approximation to high order tensors. Zbl 1001.65036
Zhang, Tong; Golub, Gene H.
2001
Numerical methods for solving linear least squares problems. Zbl 0142.11502
Golub, G.
1965
On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016
Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
2008
Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II. Zbl 0099.10903
Golub, Gene H.; Varga, Richard S.
1961
Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2006
Methods for modifying matrix factorizations. Zbl 0289.65021
Gill, P. E.; Golub, G. H.; Murray, W.; Saunders, M. A.
1974
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
Handbook series linear algebra. Linear least squares solutions by Householder transformations. Zbl 0142.11503
Businger, P.; Golub, G. H.
1965
Numerical methods for computing angles between linear subspaces. Zbl 0282.65031
Björck, Åke; Golub, Gene H.
1973
A survey of matrix inverse eigenvalue problems. Zbl 0633.65036
Boley, Daniel; Golub, Gene H.
1987
Block preconditioning for the conjugate gradient method. Zbl 0556.65022
Concus, P.; Golub, G. H.; Meurant, G.
1985
Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058
Chu, Moody T.; Golub, Gene H.
2005
Matrices, moments and quadrature with applications. Zbl 1217.65056
Golub, Gene H.; Meurant, Gérard
2010
Tikhonov regularization and total least squares. Zbl 0945.65042
Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P.
1999
The direct solution of the discrete Poisson equation on irregular regions. Zbl 0231.65083
Buzbee, B. L.; Dorr, F. W.; George, J. A.; Golub, G. H.
1971
Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014
Golub, Gene; Pereyra, Victor
2003
Structured inverse eigenvalue problems. Zbl 1105.65326
Chu, Moody T.; Golub, Gene H.
2002
Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method. Zbl 0385.65048
Concus, P.; Golub, G. H.; O’Leary, D. P.
1978
On solving block-structured indefinite linear systems. Zbl 1036.65033
Golub, Gene H.; Greif, Chen
2003
The numerically stable reconstruction of a Jacobi matrix from spectral data. Zbl 0388.15010
de Boor, C.; Golub, G. H.
1978
Ill-conditioned eigensystems and the computation of the Jordan canonical form. Zbl 0341.65027
Golub, G. H.; Wilkinson, J. H.
1976
Matrices, moments and quadrature. Zbl 0795.65019
Golub, G. H.; Meurant, Gerard
1994
Least-squares fitting of circles and ellipses. Zbl 0817.65008
Gander, Walter; Golub, Gene H.; Strebel, Rolf
1994
Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015
Benzi, Michele; Gander, Martin J.; Golub, Gene H.
2003
Iterative solution of linear systems. Zbl 0762.65019
Freund, Roland W.; Golub, Gene H.; Nachtigal, Noël M.
1992
Matrix computations. 3rd ed. Zbl 1118.65316
Golub, Gene; Van Loan, Charles F.
2007
An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053
Golub, Gene H.; Wathen, Andrew J.
1998
The Block Lanczos method for computing eigenvalues. Zbl 0407.68040
Golub, G. H.; Underwood, R.
1977
Scientific computing. An introduction with parallel computing. Zbl 0790.65001
Golub, Gene; Ortega, James M.
1993
Adaptive methods for the computation of PageRank. Zbl 1091.68044
Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene
2004
Golub, Gene H.; von Matt, Urs
1991
The simplex method of linear programming using LU decomposition. Zbl 0181.19104
Bartels, R. H.; Golub, G. H.
1969
Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041
Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina
2005
Estimation of the $$L$$-curve via Lanczos bidiagonalization. Zbl 0945.65044
Calvetti, D.; Golub, G. H.; Reichel, L.
1999
An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034
Golub, G. H.; Greif, C.
2006
Some large-scale matrix computation problems. Zbl 0870.65035
Bai, Zhaojun; Fahey, Mark; Golub, Gene
1996
An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017
Golub, Gene H.; Ye, Qiang
2002
Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050
Golub, G. H.; Meurant, G.
1997
A constrained eigenvalue problem. Zbl 0666.15006
Gander, Walter; Golub, Gene H.; von Matt, Urs
1989
A stable numerical method for inverting shape from moments. Zbl 0956.65030
Golub, Gene H.; Milanfar, Peyman; Varah, James
2000
A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Zbl 0623.15020
Golub, G. H.; Hoffman, Alan; Stewart, G. W.
1987
Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054
Benzi, Michele; Golub, Gene H.
1999
Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. Zbl 0673.65017
Golub, Gene H.; O’Leary, Dianne P.
1989
Calculation of Gauss quadratures with multiple free and fixed knots. Zbl 0525.65010
Golub, G. H.; Kautsky, J.
1983
Scientific computing and differential equations: an introduction to numerical methods. Rev. ed. Zbl 0749.65041
Golub, Gene H.; Ortega, James M.
1992
Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022
Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L.
2000
Eigenvalue computation in the 20th century. Zbl 0965.65057
Golub, Gene H.; van der Vorst, Henk A.
2000
A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. Zbl 0466.65022
Golub, Gene H.; Luk, Franklin T.; Overton, Michael L.
1981
Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022
Golub, Gene H.; Ye, Qiang
2000
On the calculation of Jacobi matrices. Zbl 0512.65030
Kautsky, J.; Golub, G. H.
1983
Adaptively preconditioned GMRES algorithms. Zbl 0954.65026
Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L.
1999
Imposing curvature restrictions on flexible functional forms. Zbl 0573.62098
Gallant, A. Ronald; Golub, Gene H.
1984
On the solution of large, structured linear complementarity problems: the block partitioned case. Zbl 0391.90087
Cottle, Richard W.; Golub, Gene H.; Sacher, Richard S.
1978
Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021
Elman, Howard C.; Golub, Gene H.
1990
Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. Zbl 0245.65043
Concus, Paul; Golub, Gene H.
1973
The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Zbl 0661.65033
Golub, Gene H.; Overton, Michael L.
1988
Note on the iterative refinement of least squares solution. Zbl 0156.16106
Golub, G. H.; Wilkinson, J. H.
1966
On Fourier-Toeplitz methods for separable elliptic problems. Zbl 0277.65065
Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O.
1974
Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains. Zbl 0594.60072
Golub, Gene H.; Meyer, Carl D. jun.
1986
The restricted singular value decomposition: Properties and applications. Zbl 0738.15006
De Moor, Bart L. R.; Golub, Gene H.
1991
A rank-one reduction formula and its applications to matrix factorizations. Zbl 0844.65033
Chu, Moody T.; Funderlic, Robert E.; Golub, Gene H.
1995
Perturbation analysis of the canonical correlations of matrix pairs. Zbl 0811.15011
Golub, Gene H.; Zha, Hongyuan
1994
A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038
Botchev, Mike A.; Golub, Gene H.
2006
A generalized conjugate gradient method for nonsymmetric systems of linear equations. Zbl 0344.65020
Concus, Paul; Golub, Gene H.
1976
Matrix computations. Paperback ed., 4th printing. Zbl 0592.65011
Golub, Gene H.; Van Loan, Charles F.
1985
Regularization by truncated total least squares. Zbl 0891.65040
Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P.
1997
Estimates in quadratic formulas. Zbl 0822.65022
Golub, Gene H.; Strakoš, Zdeněk
1994
Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027
Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun
2008
Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032
Golub, Gene H.; Ye, Qiang
2000
On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. Zbl 0646.65033
Arbenz, Peter; Golub, Gene H.
1988
On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041
Golub, Gene H.; Vanderstraeten, Denis
2000
First international symposium on domain decomposition methods for partial differential equations (Proceedings, Paris, France, January 7-9, 1987). Zbl 0649.00019
1988
Tikhonov regularization for large scale problems. Zbl 0927.65058
Golub, Gene H.; von Matt, Urs
1998
Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048
Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H.
2004
Numerical techniques in mathematical programming. Zbl 0228.90030
Bartels, R. H.; Golub, G. H.; Saunders, M. A.
1970
Matrix computations. 4th ed. Zbl 1268.65037
Golub, Gene H.; Van Loan, Charles F.
2013
Matrices, moments and quadrature with applications. Zbl 1217.65056
Golub, Gene H.; Meurant, Gérard
2010
Solving ellipsoid-constrained integer least squares problems. Zbl 1195.65049
Chang, Xiao-Wen; Golub, Gene H.
2010
The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032
Golub, Gene; Uhlig, Frank
2009
A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. Zbl 1186.65046
Vandebril, Raf; Golub, Gene; van Barel, Marc
2009
Symmetric tensors and symmetric tensor rank. Zbl 1181.15014
Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard
2008
On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016
Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
2008
Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027
Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun
2008
Continuous methods for symmetric generalized eigenvalue problems. Zbl 1140.65029
Gao, Xing-Bao; Golub, Gene H.; Liao, Li-Zhi
2008
Approximation of the scattering amplitude and linear systems. Zbl 1188.65032
Golub, Gene H.; Stoll, Martin; Wathen, Andy
2008
Towards a backward perturbation analysis for data least squares problems. Zbl 1176.65047
Chang, X.-W.; Golub, G. H.; Paige, C. C.
2008
Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022
Bai, Zhongzhi; Golub, Gene H.
2007
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2007
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
Matrix computations. 3rd ed. Zbl 1118.65316
Golub, Gene; Van Loan, Charles F.
2007
Spectral analysis of a preconditioned iterative method for the convection-diffusion equation. Zbl 1140.65024
Bertaccini, Daniele; Golub, Gene H.; Serra-Capizzano, Stefano
2007
On the numerical condition of a generalized Hankel eigenvalue problem. Zbl 1121.65036
Beckermann, B.; Golub, G. H.; Labahn, G.
2007
A hybrid approach combining Chebyshev filter and conjugate gradient for solving linear systems with multiple right-hand sides. Zbl 1151.65319
Golub, Gene H.; Ruiz, Daniel; Touhami, Ahmed
2007
A two-stage algorithm for computing PageRank and multistage generalizations. Zbl 1221.68041
Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A.
2007
A two-stage algorithm for computing pagerank and multistage generalizations. Zbl 1206.68050
Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A.
2007
Milestones in matrix computation. The selected works of Gene H. Golub. With commentaries by Anne Greenbaum, Åke Björk, Nicholas Higham, Walter Gautschi and G. W. Stewart. Edited by Raymond H. Chan, Chen Greif, and Dianne P. O’Leary. Zbl 1121.65031
Golub, Gene H.
2007
Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
2006
An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034
Golub, G. H.; Greif, C.
2006
A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038
Botchev, Mike A.; Golub, Gene H.
2006
An algebraic analysis of a block diagonal preconditioner for saddle point systems. Zbl 1105.65048
Golub, Gene H.; Greif, Chen; Varah, James M.
2006
Continuous methods for extreme and interior eigenvalue problems. Zbl 1092.65029
Golub, Gene H.; Liao, Li-Zhi
2006
On a generalized eigenvalue problem for nonsquare pencils. Zbl 1128.15004
Chu, Delin; Golub, Gene H.
2006
Some observations on local least squares. Zbl 1103.65041
Bartels, R. H.; Golub, G. H.; Samavati, F. F.
2006
Numerical solution of saddle point problems. Zbl 1115.65034
Benzi, Michele; Golub, Gene H.; Liesen, Jörg
2005
Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028
Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng
2005
Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058
Chu, Moody T.; Golub, Gene H.
2005
Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041
Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina
2005
A bibliography on semiseparable matrices. Zbl 1168.15312
Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N.
2005
The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach. Zbl 1100.65035
Boutry, Gregory; Elad, Michael; Golub, Gene H.; Milanfar, Peyman
2005
How to deduce a proper eigenvalue cluster from a proper singular value cluster in the nonnormal case. Zbl 1088.65031
Serra-Capizzano, Stefano; Bertaccini, Daniele; Golub, Gene H.
2005
Multidimensional integral inversion, with applications in shape reconstruction. Zbl 1099.65128
Cuyt, Annie; Golub, Gene; Milanfar, Peyman; Verdonk, Brigitte
2005
A bibliography on semiseparable matrices. Zbl 1168.15306
Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola
2005
A subspace approximation method for the quadratic eigenvalue problem. Zbl 1079.65039
Holz, U. B.; Golub, G. H.; Law, K. H.
2005
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025
Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu
2004
A preconditioner for generalized saddle point problems. Zbl 1082.65034
Benzi, Michele; Golub, Gene H.
2004
Adaptive methods for the computation of PageRank. Zbl 1091.68044
Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene
2004
Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048
Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H.
2004
Shape from moments – an estimation theory perspective. Zbl 1369.62145
Elad, Michael; Milanfar, Peyman; Golub, Gene H.
2004
Semi-conjugate direction methods for real positive definite systems. Zbl 1052.65026
Yuan, J. Y.; Golub, G. H.; Plemmons, R. J.; Cecilio, W. A. G.
2004
Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032
Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K.
2003
Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014
Golub, Gene; Pereyra, Victor
2003
On solving block-structured indefinite linear systems. Zbl 1036.65033
Golub, Gene H.; Greif, Chen
2003
Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015
Benzi, Michele; Gander, Martin J.; Golub, Gene H.
2003
Scaling by binormalization. Zbl 1050.65049
Livne, Oren E.; Golub, Gene H.
2003
The spectrum of a modified linear pencil. Zbl 1054.65033
Elhay, S.; Golub, G. H.; Ram, Y. M.
2003
Structured inverse eigenvalue problems. Zbl 1105.65326
Chu, Moody T.; Golub, Gene H.
2002
An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017
Golub, Gene H.; Ye, Qiang
2002
Symmetric-triangular decomposition and its applications. I: Theorems and algorithms. Zbl 1017.65020
Golub, Gene H.; Yuan, Jin-Yun
2002
Block orderings for tensor-product grids in two and three dimensions. Zbl 1002.65041
Golub, Gene H.; Greif, Chen; Varah, James M.
2002
SOR-like methods for augmented systems. Zbl 0991.65036
Golub, Gene H.; Wu, X.; Yuan, Jin-Yun
2001
Rank-one approximation to high order tensors. Zbl 1001.65036
Zhang, Tong; Golub, Gene H.
2001
From numerical analysis to computational science. Zbl 1047.65504
Engquist, Björn; Golub, Gene
2001
Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. Zbl 1037.68784
Nguyen, Nhat; Milanfar, Peyman; Golub, Gene
2001
A computationally efficient superresolution image reconstruction algorithm. Zbl 1040.68567
Nguyen, Nhat; Milanfar, Peyman; Golub, Gene
2001
A parallel balance scheme for banded linear systems. Zbl 1055.65044
Golub, Gene H.; Sameh, Ahmed H.; Sarin, Vivek
2001
A note on preconditioning for indefinite linear systems. Zbl 0959.65063
Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J.
2000
A stable numerical method for inverting shape from moments. Zbl 0956.65030
Golub, Gene H.; Milanfar, Peyman; Varah, James
2000
Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022
Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L.
2000
Eigenvalue computation in the 20th century. Zbl 0965.65057
Golub, Gene H.; van der Vorst, Henk A.
2000
Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022
Golub, Gene H.; Ye, Qiang
2000
Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032
Golub, Gene H.; Ye, Qiang
2000
On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041
Golub, Gene H.; Vanderstraeten, Denis
2000
Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations. Zbl 0948.65033
Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan
2000
Computing the SVD of a general matrix product/quotient. Zbl 0969.65032
Golub, Gene; Sølna, Knut; Van Dooren, Paul
2000
A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118
Chan, Tony F.; Golub, Gene H.; Mulet, Pep
1999
Tikhonov regularization and total least squares. Zbl 0945.65042
Golub, Gene H.; Hansen, Per Christian; O&rsquo;Leary, Dianne P.
1999
Estimation of the $$L$$-curve via Lanczos bidiagonalization. Zbl 0945.65044
Calvetti, D.; Golub, G. H.; Reichel, L.
1999
Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054
Benzi, Michele; Golub, Gene H.
1999
Adaptively preconditioned GMRES algorithms. Zbl 0954.65026
Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L.
1999
On some eigenvector-eigenvalue relations. Zbl 0929.15008
Elhay, S.; Gladwell, G. M. L.; Golub, G. H.; Ram, Y. M.
1999
An efficient algorithm for a bounded errors-in-variables model. Zbl 0957.65070
Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H.
1999
Subspace iterative methods for eigenvalue problems. Zbl 0932.65044
Zhang, T.; Golub, G. H.; Law, K. H.
1999
Applications and computation of orthogonal polynomials. Conference at the Mathematical Research Institute Oberwolfach, Germany, March 22–29, 1998. Dedicated to the memory of Günther Hämmerlin. Zbl 0919.00065
1999
A computable error bound for matrix functionals. Zbl 0937.65054
Calvetti, D.; Golub, G. H.; Reichel, L.
1999
An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053
Golub, Gene H.; Wathen, Andrew J.
1998
Tikhonov regularization for large scale problems. Zbl 0927.65058
Golub, Gene H.; von Matt, Urs
1998
Solution of biharmonic equations with application to radar imaging. Zbl 0933.65128
Andersson, Lars-Erik; Elfving, Tommy; Golub, Gene H.
1998
Parameter estimation in the presence of bounded data uncertainties. Zbl 0914.65147
Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H.
1998
A fast Poisson solver for the finite difference solution of the incompressible Navier-Stokes equations. Zbl 0957.76053
Golub, Gene H.; Huang, Lan Chieh; Simon, Horst; Tang, Wei-Pai
1998
Rank modifications of semidefinite matrices associated with a secant update formula. Zbl 0922.65031
Chu, Moody T.; Funderlic, R. E.; Golub, Gene H.
1998
On the homotopy method for perturbed symmetric generalized eigenvalue problems. Zbl 0917.65035
Zhang, T.; Law, K. H.; Golub, G. H.
1998
Inner and outer iterations for the Chebyshev algorithm. Zbl 0911.65024
Giladi, Eldar; Golub, Gene H.; Keller, Joseph B.
1998
Cyclic reduction – history and applications. Zbl 0921.65023
Gander, Walter; Golub, Gene H.
1998
Scientific computing, WSC ’97. Proceedings of the workshop held in Hong Kong, March 10–12, 1997. Zbl 0910.00057
1998
Efficient solution of the Jacobian system in Newton’s method close to a root. Zbl 0921.65039
Drexler, Michael; Golub, Gene H.
1998
Eigenvalue perturbation and generalized Krylov subspace method. Zbl 0931.65039
Zhang, T.; Golub, G. H.; Law, K. H.
1998
Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050
Golub, G. H.; Meurant, G.
1997
Regularization by truncated total least squares. Zbl 0891.65040
Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O&rsquo;Leary, D. P.
1997
Generalized cross-validation for large scale problems. Zbl 0878.65032
Golub, Gene H.; von Matt, Urs
1997
Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013
Bai, Zhaojun; Golub, Gene H.
1997
On a variational formulation of the generalized singular value decomposition. Zbl 0891.65038
Chu, Moody T.; Funderlic, Robert. E.; Golub, Gene H.
1997
Closer to the solution: Iterative linear solvers. Zbl 0881.65025
Golub, Gene H.; van der Vorst, Henk A.
1997
150 years old and still alive: Eigenproblems. Zbl 0881.65026
van der Vorst, Henk A.; Golub, Gene H.
1997
Efficient algorithms for least squares type problems with bounded uncertainties. Zbl 0892.62038
Chandrasekaran, Shivkumar; Golub, Gene H.; Gu, Ming; Sayed, Ali H.
1997
Matrix computations. 3rd ed. Zbl 0865.65009
Golub, Gene; Van Loan, Charles F.
1996
...and 135 more Documents
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### Cited by 14,073 Authors

 122 Reichel, Lothar 97 Wei, Yimin 67 Bai, Zhongzhi 66 Huang, Ting-Zhu 65 Pan, Victor Yakovlevich 63 Golub, Gene Howard 63 Ma, Changfeng 61 Zhang, Guofeng 56 Jódar Sanchez, Lucas Antonio 47 Benner, Peter 43 Khojasteh Salkuyeh, Davod 42 Evans, David John 41 Ng, Michael Kwok-Po 40 Serra-Capizzano, Stefano 38 Van Barel, Marc 37 Axelsson, Axel Owe Holger 37 Dehghan Takht Fooladi, Mehdi 36 Benzi, Michele 36 Liang, Zhaozheng 35 Mehrmann, Volker 35 Simoncini, Valeria 34 Cao, Yang 34 Wu, Shiliang 33 Jbilou, Khalide 32 Li, Cuixia 32 Van Dooren, Paul M. 32 Van Huffel, Sabine 31 Lin, Wen-Wei 31 Milovanović, Gradimir V. 30 Chen, Guoliang 30 Wu, Yujiang 29 Qi, Liqun 28 Jia, Zhongxiao 28 Wei, Musheng 27 Jin, Xiaoqing 27 Yang, Aili 26 Li, Rencang 26 Nakatsukasa, Yuji 25 Dai, Hua 25 Huang, Zhengge 25 Saad, Yousef 24 Martínez, José Mario 24 Stoll, Martin 23 Calvetti, Daniela 23 Kressner, Daniel 23 Lu, Linzhang 23 Mastronardi, Nicola 23 Vandebril, Raf 22 Bini, Dario Andrea 22 Cui, Jingjing 22 Gu, Chuanqing 22 Hu, Xiyan 22 Lin, Yiqin 22 Mitrouli, Marilena 22 Sadkane, Miloud 22 Wu, Gang 22 Zheng, Bing 21 Gemignani, Luca 21 Hajarian, Masoud 21 Li, Wen 21 Sadok, Hassane 20 Higham, Nicholas J. 20 Nagy, James Gerard 20 Rojo, Oscar L. 20 Toutounian, Faezeh 20 Wathen, Andrew John 20 Xiang, Hua 20 Xu, Zhong 19 Chen, Fang 19 Gondzio, Jacek 19 Hansen, Per Christian 19 Miao, Shu-Xin 19 O’Leary, Dianne P. 19 Plemmons, Robert James 19 Rodriguez, Giuseppe 19 Wang, Xiang 19 Zhang, Lei 18 Bai, Zhaojun 18 Bai, Zhengjian 18 Gautschi, Walter 18 Hadjidimos, Apostolos 18 Verhaegen, Michel 18 Ye, Qiang 17 Ballico, Edoardo 17 Barlow, Jesse L. 17 Chu, Delin 17 Chu, Moody T. 17 De Moor, Bart L. R. 17 Fan, Hongtao 17 King-wah Chu, Eric 17 Paige, Christopher C. 17 Spalević, Miodrag M. 17 Wang, Ligong 17 Wu, Qingbiao 17 Zha, Hongyuan 17 Zhang, Jun 17 Zhang, Lei-Hong 16 Brezinski, Claude 16 Cao, Zhihao 16 Chan, Raymond Hon-Fu ...and 13,973 more Authors
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### Cited in 717 Serials

 1,014 Linear Algebra and its Applications 784 Journal of Computational and Applied Mathematics 520 Applied Mathematics and Computation 376 Computers & Mathematics with Applications 357 Journal of Computational Physics 345 Numerical Algorithms 283 Numerische Mathematik 271 Computer Methods in Applied Mechanics and Engineering 258 Applied Numerical Mathematics 246 SIAM Journal on Scientific Computing 242 BIT 209 SIAM Journal on Matrix Analysis and Applications 206 Mathematics of Computation 192 Numerical Linear Algebra with Applications 190 International Journal of Computer Mathematics 163 Automatica 128 Journal of Scientific Computing 115 Computational Statistics and Data Analysis 114 Applied Mathematics Letters 100 Computational Optimization and Applications 88 International Journal of Control 87 Computing 87 Computational and Applied Mathematics 80 Journal of Optimization Theory and Applications 80 Mathematical Programming. Series A. Series B 77 Calcolo 69 Mathematical Problems in Engineering 65 Mathematical and Computer Modelling 64 Pattern Recognition 63 Linear and Multilinear Algebra 63 Optimization Methods & Software 61 Engineering Analysis with Boundary Elements 60 International Journal for Numerical Methods in Engineering 60 Advances in Computational Mathematics 59 Mathematics and Computers in Simulation 58 Systems & Control Letters 57 Journal of Econometrics 54 Journal of Mathematical Analysis and Applications 53 Applied Mathematical Modelling 52 Journal of Mathematical Imaging and Vision 50 Computer Physics Communications 45 Journal of Statistical Computation and Simulation 45 East Asian Journal on Applied Mathematics 44 Mathematical Programming 43 Computers and Fluids 41 Signal Processing 41 Journal of Applied Mathematics and Computing 40 Circuits, Systems, and Signal Processing 40 SIAM Journal on Optimization 39 Journal of the Franklin Institute 37 Theoretical Computer Science 37 Applied and Computational Harmonic Analysis 36 Inverse Problems 36 Japan Journal of Industrial and Applied Mathematics 36 SIAM Journal on Imaging Sciences 35 The Annals of Statistics 34 Computational Mechanics 34 European Journal of Operational Research 33 Journal of Multivariate Analysis 32 SIAM Journal on Numerical Analysis 31 Numerical Functional Analysis and Optimization 31 Machine Learning 31 Journal of Global Optimization 30 Multidimensional Systems and Signal Processing 30 Statistics and Computing 29 International Journal for Numerical Methods in Fluids 29 Computational Geosciences 29 Inverse Problems in Science and Engineering 27 Computer Aided Geometric Design 26 Information Sciences 26 Parallel Algorithms and Applications 26 Foundations of Computational Mathematics 25 International Journal of Systems Science 25 Journal of Approximation Theory 25 Journal of Economic Dynamics & Control 25 Neural Networks 25 International Journal of Computer Vision 24 Journal of Mathematical Physics 24 Journal of Statistical Planning and Inference 24 SIAM Review 24 The Annals of Applied Statistics 23 Journal of Inequalities and Applications 23 Journal of Applied Mathematics 23 Frontiers of Mathematics in China 23 Science China. Mathematics 22 Journal of Fluid Mechanics 22 Journal of Symbolic Computation 21 Mathematical Biosciences 21 Physica D 21 Journal of Complexity 21 Annals of Operations Research 21 Neural Computation 21 Communications in Statistics. Theory and Methods 21 Journal of Machine Learning Research (JMLR) 21 BIT. Nordisk Tidskrift for Informationsbehandling 20 Computational Statistics 20 Automation and Remote Control 20 Communications in Statistics. Simulation and Computation 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 617 more Serials
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### Cited in 61 Fields

 7,549 Numerical analysis (65-XX) 2,422 Linear and multilinear algebra; matrix theory (15-XX) 1,145 Statistics (62-XX) 1,100 Operations research, mathematical programming (90-XX) 1,049 Partial differential equations (35-XX) 932 Computer science (68-XX) 853 Systems theory; control (93-XX) 716 Fluid mechanics (76-XX) 512 Information and communication theory, circuits (94-XX) 448 Mechanics of deformable solids (74-XX) 355 Probability theory and stochastic processes (60-XX) 346 Approximations and expansions (41-XX) 340 Calculus of variations and optimal control; optimization (49-XX) 330 Ordinary differential equations (34-XX) 292 Biology and other natural sciences (92-XX) 230 Operator theory (47-XX) 202 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 183 Combinatorics (05-XX) 155 Quantum theory (81-XX) 154 Harmonic analysis on Euclidean spaces (42-XX) 151 Optics, electromagnetic theory (78-XX) 138 Special functions (33-XX) 138 Dynamical systems and ergodic theory (37-XX) 138 Geophysics (86-XX) 121 Mechanics of particles and systems (70-XX) 110 Statistical mechanics, structure of matter (82-XX) 106 Integral equations (45-XX) 89 Algebraic geometry (14-XX) 83 Real functions (26-XX) 81 Functions of a complex variable (30-XX) 69 Number theory (11-XX) 63 Functional analysis (46-XX) 59 Differential geometry (53-XX) 57 Field theory and polynomials (12-XX) 57 Classical thermodynamics, heat transfer (80-XX) 52 Integral transforms, operational calculus (44-XX) 41 Commutative algebra (13-XX) 38 Difference and functional equations (39-XX) 36 Potential theory (31-XX) 34 Global analysis, analysis on manifolds (58-XX) 29 Convex and discrete geometry (52-XX) 24 Geometry (51-XX) 23 Astronomy and astrophysics (85-XX) 20 History and biography (01-XX) 18 General and overarching topics; collections (00-XX) 18 Group theory and generalizations (20-XX) 16 Measure and integration (28-XX) 16 Manifolds and cell complexes (57-XX) 15 General topology (54-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Sequences, series, summability (40-XX) 11 Topological groups, Lie groups (22-XX) 9 Associative rings and algebras (16-XX) 8 Mathematical logic and foundations (03-XX) 7 Relativity and gravitational theory (83-XX) 6 Nonassociative rings and algebras (17-XX) 5 Algebraic topology (55-XX) 4 Mathematics education (97-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 General algebraic systems (08-XX) 3 Abstract harmonic analysis (43-XX)

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