Evstigneev, N. M.; Ryabkov, O. I.; Bocharov, A. N.; Petrovskiy, V. P.; Teplyakov, I. O. Compensated summation and dot product algorithms for floating-point vectors on parallel architectures: error bounds, implementation and application in the Krylov subspace methods. (English) Zbl 1492.65374 J. Comput. Appl. Math. 414, Article ID 114434, 37 p. (2022). MSC: 65Y10 65Y05 65G50 65F08 PDFBibTeX XMLCite \textit{N. M. Evstigneev} et al., J. Comput. Appl. Math. 414, Article ID 114434, 37 p. (2022; Zbl 1492.65374) Full Text: DOI
Gu, Xian-Ming; Sun, Hai-Wei; Zhang, Yanzhi; Zhao, Yong-Liang Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian. (English) Zbl 1512.65303 Math. Methods Appl. Sci. 44, No. 1, 441-463 (2021). MSC: 65R20 35R11 65N06 65F08 PDFBibTeX XMLCite \textit{X.-M. Gu} et al., Math. Methods Appl. Sci. 44, No. 1, 441--463 (2021; Zbl 1512.65303) Full Text: DOI arXiv
Al-Baali, Mehiddin; Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo A class of approximate inverse preconditioners based on Krylov-subspace methods for large-scale nonconvex optimization. (English) Zbl 1480.90169 SIAM J. Optim. 30, No. 3, 1954-1979 (2020). Reviewer: Paulo Mbunga (Kiel) MSC: 90C06 90C26 90C30 PDFBibTeX XMLCite \textit{M. Al-Baali} et al., SIAM J. Optim. 30, No. 3, 1954--1979 (2020; Zbl 1480.90169) Full Text: DOI
O’Hearn, Kurt A.; Alperen, Abdullah; Aktulga, Hasan Metin Fast solvers for charge distribution models on shared memory platforms. (English) Zbl 1431.65026 SIAM J. Sci. Comput. 42, No. 1, C1-C22 (2020). MSC: 65F08 65F10 65F50 PDFBibTeX XMLCite \textit{K. A. O'Hearn} et al., SIAM J. Sci. Comput. 42, No. 1, C1--C22 (2020; Zbl 1431.65026) Full Text: DOI
Mohamed, M. Shadi; Seaid, Mohammed; Bouhamidi, Abderrahman Iterative solvers for generalized finite element solution of boundary-value problems. (English) Zbl 1513.65081 Numer. Linear Algebra Appl. 25, No. 6, e2205, 18 p. (2018). MSC: 65F10 65N30 PDFBibTeX XMLCite \textit{M. S. Mohamed} et al., Numer. Linear Algebra Appl. 25, No. 6, e2205, 18 p. (2018; Zbl 1513.65081) Full Text: DOI Link
Jarlebring, Elias; Mele, Giampaolo; Palitta, Davide; Ringh, Emil Krylov methods for low-rank commuting generalized Sylvester equations. (English) Zbl 07031731 Numer. Linear Algebra Appl. 25, No. 6, e2176, 17 p. (2018). MSC: 65F45 65F55 PDFBibTeX XMLCite \textit{E. Jarlebring} et al., Numer. Linear Algebra Appl. 25, No. 6, e2176, 17 p. (2018; Zbl 07031731) Full Text: DOI arXiv
Neuenhofen, Martin P.; Greif, Chen Mstab: stabilized induced dimension reduction for Krylov subspace recycling. (English) Zbl 1390.93355 SIAM J. Sci. Comput. 40, No. 2, B554-B571 (2018). MSC: 93C05 65F10 93A15 65F50 65N22 PDFBibTeX XMLCite \textit{M. P. Neuenhofen} and \textit{C. Greif}, SIAM J. Sci. Comput. 40, No. 2, B554--B571 (2018; Zbl 1390.93355) Full Text: DOI
Powell, C. E.; Silvester, D.; Simoncini, V. An efficient reduced basis solver for stochastic Galerkin matrix equations. (English) Zbl 1381.35257 SIAM J. Sci. Comput. 39, No. 1, A141-A163 (2017). MSC: 35R60 60H35 65N30 65F10 65N22 PDFBibTeX XMLCite \textit{C. E. Powell} et al., SIAM J. Sci. Comput. 39, No. 1, A141--A163 (2017; Zbl 1381.35257) Full Text: DOI
Zhu, Yao; Sameh, Ahmed H. \(\text{PSPIKE}+\): A family of parallel hybrid sparse linear system solvers. (English) Zbl 1355.65056 J. Comput. Appl. Math. 311, 682-703 (2017). MSC: 65F10 65F08 65F50 65Y05 PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{A. H. Sameh}, J. Comput. Appl. Math. 311, 682--703 (2017; Zbl 1355.65056) Full Text: DOI
Keuchel, Sören; Biermann, Jan; von Estorff, Otto A combination of the fast multipole boundary element method and Krylov subspace recycling solvers. (English) Zbl 1403.65202 Eng. Anal. Bound. Elem. 65, 136-146 (2016). MSC: 65N38 65N22 PDFBibTeX XMLCite \textit{S. Keuchel} et al., Eng. Anal. Bound. Elem. 65, 136--146 (2016; Zbl 1403.65202) Full Text: DOI
Li, Ruipeng; Xi, Yuanzhe; Saad, Yousef Schur complement-based domain decomposition preconditioners with low-rank corrections. (English) Zbl 1399.65238 Numer. Linear Algebra Appl. 23, No. 4, 706-729 (2016). Reviewer: Miroslav Tůma (Praha) MSC: 65M55 65F08 65F10 65F50 35J05 15A18 PDFBibTeX XMLCite \textit{R. Li} et al., Numer. Linear Algebra Appl. 23, No. 4, 706--729 (2016; Zbl 1399.65238) Full Text: DOI arXiv
Grigori, Laura; Nataf, Frédéric; Qu, Long Overlapping for preconditioners based on incomplete factorizations and nested arrow form. (English) Zbl 1363.65044 Numer. Linear Algebra Appl. 22, No. 1, 48-75 (2015). MSC: 65F08 65F10 65N55 PDFBibTeX XMLCite \textit{L. Grigori} et al., Numer. Linear Algebra Appl. 22, No. 1, 48--75 (2015; Zbl 1363.65044) Full Text: DOI
Weller, Stephan; Basting, Steffen Efficient preconditioning of variational time discretization methods for parabolic partial differential equations. (English) Zbl 1315.65031 ESAIM, Math. Model. Numer. Anal. 49, No. 2, 331-347 (2015). MSC: 65F08 35K20 65M60 35K05 PDFBibTeX XMLCite \textit{S. Weller} and \textit{S. Basting}, ESAIM, Math. Model. Numer. Anal. 49, No. 2, 331--347 (2015; Zbl 1315.65031) Full Text: DOI
Carson, Erin; Knight, Nicholas; Demmil, James An efficient deflation technique for the communication-avoiding conjugate gradient. (English) Zbl 1312.65040 ETNA, Electron. Trans. Numer. Anal. 43(2014-2015), 125-141 (2014). MSC: 65F10 65F08 65F50 65Y05 65Y20 PDFBibTeX XMLCite \textit{E. Carson} et al., ETNA, Electron. Trans. Numer. Anal. 43, 125--141 (2014; Zbl 1312.65040) Full Text: EMIS
Slaybaugh, R. N.; Evans, T. M.; Davidson, G. G.; Wilson, P. P. H. Multigrid in energy preconditioner for Krylov solvers. (English) Zbl 1297.65207 J. Comput. Phys. 242, 405-419 (2013). MSC: 65R20 45K05 65F08 65F10 65F15 82D75 PDFBibTeX XMLCite \textit{R. N. Slaybaugh} et al., J. Comput. Phys. 242, 405--419 (2013; Zbl 1297.65207) Full Text: DOI arXiv
Camata, J. J.; Rossa, A. L.; Valli, Andrea M. P.; Catabriga, Lucia; Carey, Graham F.; Coutinho, Alvaro L. G. A. Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions. (English) Zbl 1253.76090 Int. J. Numer. Methods Fluids 69, No. 4, 802-823 (2012). MSC: 76M25 65M22 65F08 PDFBibTeX XMLCite \textit{J. J. Camata} et al., Int. J. Numer. Methods Fluids 69, No. 4, 802--823 (2012; Zbl 1253.76090) Full Text: DOI
Curtis, Frank E.; Huber, Johannes; Schenk, Olaf; Wächter, Andreas A note on the implementation of an interior-point algorithm for nonlinear optimization with inexact step computations. (English) Zbl 1255.49043 Math. Program. 136, No. 1 (B), 209-227 (2012). MSC: 49M05 49M15 49M37 65F10 65K05 65N22 90C06 90C26 90C30 90C51 90C90 PDFBibTeX XMLCite \textit{F. E. Curtis} et al., Math. Program. 136, No. 1 (B), 209--227 (2012; Zbl 1255.49043) Full Text: DOI
Aktulga, Hasan Metin; Pandit, Sagar A.; van Duin, Adri C. T.; Grama, Ananth Y. Reactive molecular dynamics: numerical methods and algorithmic techniques. (English) Zbl 1387.65128 SIAM J. Sci. Comput. 34, No. 1, C1-C23 (2012). MSC: 65P10 65F08 65F10 65F50 70F10 81V55 PDFBibTeX XMLCite \textit{H. M. Aktulga} et al., SIAM J. Sci. Comput. 34, No. 1, C1--C23 (2012; Zbl 1387.65128) Full Text: DOI Link
Sleijpen, Gerard L. G.; Van Gijzen, Martin B. Exploiting BiCGSTAB(\(\ell\)) strategies to induce dimension reduction. (English) Zbl 1220.65042 SIAM J. Sci. Comput. 32, No. 5, 2687-2709 (2010). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 PDFBibTeX XMLCite \textit{G. L. G. Sleijpen} and \textit{M. B. Van Gijzen}, SIAM J. Sci. Comput. 32, No. 5, 2687--2709 (2010; Zbl 1220.65042) Full Text: DOI Link
Sleijpen, Gerard L. G.; Sonneveld, Peter; van Gijzen, Martin B. Bi-CGSTAB as an induced dimension reduction method. (English) Zbl 1200.65024 Appl. Numer. Math. 60, No. 11, 1100-1114 (2010). MSC: 65F10 65F15 65N25 PDFBibTeX XMLCite \textit{G. L. G. Sleijpen} et al., Appl. Numer. Math. 60, No. 11, 1100--1114 (2010; Zbl 1200.65024) Full Text: DOI
Reps, Bram; Vanroose, Wim; bin Zubair, Hisham On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning. (English) Zbl 1210.65182 J. Comput. Phys. 229, No. 22, 8384-8405 (2010). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N06 35J05 65N55 65F08 65F10 PDFBibTeX XMLCite \textit{B. Reps} et al., J. Comput. Phys. 229, No. 22, 8384--8405 (2010; Zbl 1210.65182) Full Text: DOI arXiv
Avron, Haim; Ng, Esmond; Toledo, Sivan Using perturbed \(QR\) factorizations to solve linear least-squares problems. (English) Zbl 1195.65048 SIAM J. Matrix Anal. Appl. 31, No. 2, 674-693 (2009). Reviewer: Tzvetan Semerdjiev (Sofia) MSC: 65F20 65F10 65F22 65F50 PDFBibTeX XMLCite \textit{H. Avron} et al., SIAM J. Matrix Anal. Appl. 31, No. 2, 674--693 (2009; Zbl 1195.65048) Full Text: DOI
Benzi, Michele; Wathen, Andrew J. Some preconditiong techniques for saddle point problems. (English) Zbl 1152.65425 Schilders, Wilhelmus H. A. (ed.) et al., Model order reduction: Theory, research aspects and applications. Selected papers based on the presentations at the workshop ‘Model order reduction, coupled problems and optimization’, Leiden, The Netherlands, September 19–23, 2005. Berlin: Springer (ISBN 978-3-540-78840-9/hbk). Mathematics in Industry 13, 195-211 (2008). MSC: 65F35 65F10 PDFBibTeX XMLCite \textit{M. Benzi} and \textit{A. J. Wathen}, Math. Ind. 13, 195--211 (2008; Zbl 1152.65425)
Greif, Chen; Schötzau, Dominik Preconditioners for the discretized time-harmonic Maxwell equations in mixed form. (English) Zbl 1199.78010 Numer. Linear Algebra Appl. 14, No. 4, 281-297 (2007). MSC: 78M10 65N30 65F10 PDFBibTeX XMLCite \textit{C. Greif} and \textit{D. Schötzau}, Numer. Linear Algebra Appl. 14, No. 4, 281--297 (2007; Zbl 1199.78010) Full Text: DOI
Parks, Michael L.; De Sturler, Eric; Mackey, Greg; Johnson, Duane D.; Maiti, Spandan Recycling Krylov subspaces for sequences of linear systems. (English) Zbl 1123.65022 SIAM J. Sci. Comput. 28, No. 5, 1651-1674 (2006). MSC: 65F10 65N06 35J25 PDFBibTeX XMLCite \textit{M. L. Parks} et al., SIAM J. Sci. Comput. 28, No. 5, 1651--1674 (2006; Zbl 1123.65022) Full Text: DOI Link
Greif, Chen; Schötzau, Dominik Preconditioners for saddle point linear systems with highly singular \((1,1)\) blocks. (English) Zbl 1112.65042 ETNA, Electron. Trans. Numer. Anal. 22, 114-121 (2006). MSC: 65F35 65F10 PDFBibTeX XMLCite \textit{C. Greif} and \textit{D. Schötzau}, ETNA, Electron. Trans. Numer. Anal. 22, 114--121 (2006; Zbl 1112.65042) Full Text: EuDML
Bridson, Robert; Greif, Chen A multipreconditioned conjugate gradient algorithm. (English) Zbl 1104.65027 SIAM J. Matrix Anal. Appl. 27, No. 4, 1056-1068 (2006). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65F35 PDFBibTeX XMLCite \textit{R. Bridson} and \textit{C. Greif}, SIAM J. Matrix Anal. Appl. 27, No. 4, 1056--1068 (2006; Zbl 1104.65027) Full Text: DOI
Benzi, Michele; Golub, Gene H.; Liesen, Jörg Numerical solution of saddle point problems. (English) Zbl 1115.65034 Acta Numerica 14, 1-137 (2005). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F10 65F50 65F05 65F35 65-02 94A08 91G60 PDFBibTeX XMLCite \textit{M. Benzi} et al., Acta Numerica 14, 1--137 (2005; Zbl 1115.65034) Full Text: DOI
Rathish Kumar, B. V.; Mehra, Mani Wavelet based preconditioners for sparse linear systems. (English) Zbl 1084.65045 Appl. Math. Comput. 171, No. 1, 203-224 (2005). MSC: 65F35 65F10 65F50 65T60 PDFBibTeX XMLCite \textit{B. V. Rathish Kumar} and \textit{M. Mehra}, Appl. Math. Comput. 171, No. 1, 203--224 (2005; Zbl 1084.65045) Full Text: DOI
Flórez, E.; García, M. D.; González, L.; Montero, G. The effect of orderings on sparse approximate inverse preconditioners for non-symmetric problems. (English) Zbl 1024.65038 Adv. Eng. Softw. 33, No. 7-10, 611-619 (2002). MSC: 65F35 35J25 65F10 65F50 65N30 PDFBibTeX XMLCite \textit{E. Flórez} et al., Adv. Eng. Softw. 33, No. 7--10, 611--619 (2002; Zbl 1024.65038) Full Text: DOI
Hemmingsson-Frändén, Lina; Wathen, Andrew A nearly optimal preconditioner for the Navier-Stokes equations. (English) Zbl 1051.65056 Numer. Linear Algebra Appl. 8, No. 4, 229-243 (2001). MSC: 65F35 65F10 76D05 PDFBibTeX XMLCite \textit{L. Hemmingsson-Frändén} and \textit{A. Wathen}, Numer. Linear Algebra Appl. 8, No. 4, 229--243 (2001; Zbl 1051.65056) Full Text: DOI Link
Shadid, J. N. A fully-coupled Newton-Krylov solution method for parallel unstructured finite element fluid flow, heat and mass transfer simulations. (English) Zbl 0969.76049 Int. J. Comput. Fluid Dyn. 12, No. 3-4, 199-211 (1999). MSC: 76M10 76N15 80A20 PDFBibTeX XMLCite \textit{J. N. Shadid}, Int. J. Comput. Fluid Dyn. 12, No. 3--4, 199--211 (1999; Zbl 0969.76049) Full Text: DOI
Škerget, L.; Hriberšek, M.; Kuhn, G. Computational fluid dynamics by boundary-domain integral method. (English) Zbl 0951.76053 Int. J. Numer. Methods Eng. 46, No. 8, 1291-1311 (1999). MSC: 76M15 76D05 80A20 PDFBibTeX XMLCite \textit{L. Škerget} et al., Int. J. Numer. Methods Eng. 46, No. 8, 1291--1311 (1999; Zbl 0951.76053) Full Text: DOI
Piquet, Jean; Vasseur, Xavier Comparisons between preconditioned BICGSTAB and a multigrid method for the resolution of the pressure equation in a Navier-Stokes solver. (English) Zbl 0940.76046 Hackbusch, Wolfgang (ed.) et al., Multigrid methods V. Proceedings of the 5th European multigrid conference, held in Stuttgart, Germany, October 1-4, 1996. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 3, 225-242 (1998). MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{J. Piquet} and \textit{X. Vasseur}, Lect. Notes Comput. Sci. Eng. 3, 225--242 (1998; Zbl 0940.76046)
Chernesky, Michael P. On preconditioned Krylov subspace methods for discrete convection-diffusion problems. (English) Zbl 0881.65095 Numer. Methods Partial Differ. Equations 13, No. 4, 321-330 (1997). Reviewer: E.Schechter (Kaiserslautern) MSC: 65N06 35J25 65F10 65N12 65F35 PDFBibTeX XMLCite \textit{M. P. Chernesky}, Numer. Methods Partial Differ. Equations 13, No. 4, 321--330 (1997; Zbl 0881.65095) Full Text: DOI
Hriberšek, M.; Škerget, L. Domain decomposition methods for vorticity transport equation in boundary domain integral method. (English) Zbl 0843.76055 Aliabadi, M. H. (ed.) et al., Boundary element technology X. Proceedings of the 10th international conference, BETECH ’95, held in Liège, Belgium, September 1995. Southampton: Computational Mechanics Publications. 161-168 (1995). MSC: 76M15 76D05 PDFBibTeX XMLCite \textit{M. Hriberšek} and \textit{L. Škerget}, in: Boundary element technology X. Proceedings of the 10th international conference, BETECH '95, held in Liège, Belgium, September 1995. Southampton: Computational Mechanics Publications. 161--168 (1995; Zbl 0843.76055)
Pernice, Michael Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers. (English) Zbl 0817.65117 Keyes, David E. (ed.) et al., Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 180, 303-309 (1994). MSC: 65N55 65F35 65Y05 65F10 65N06 35J25 PDFBibTeX XMLCite \textit{M. Pernice}, Contemp. Math. 180, 303--309 (1994; Zbl 0817.65117)
Weiss, Rudiger Minimization properties and short recurrences for Krylov subspace methods. (English) Zbl 0809.65027 ETNA, Electron. Trans. Numer. Anal. 2, 57-75 (1994). MSC: 65F10 65F50 PDFBibTeX XMLCite \textit{R. Weiss}, ETNA, Electron. Trans. Numer. Anal. 2, 57--75 (1994; Zbl 0809.65027) Full Text: EuDML EMIS
Sleijpen, Gerard L. G.; Fokkema, Diederik R. BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum. (English) Zbl 0820.65016 ETNA, Electron. Trans. Numer. Anal. 1, 11-32 (1993). MSC: 65F10 PDFBibTeX XMLCite \textit{G. L. G. Sleijpen} and \textit{D. R. Fokkema}, ETNA, Electron. Trans. Numer. Anal. 1, 11--32 (1993; Zbl 0820.65016) Full Text: EuDML EMIS
Chan, Tony F.; Jackson, Kenneth R. The use of iterative linear-equation solvers in codes for large systems of stiff IVPs for ODEs. (English) Zbl 0611.65050 SIAM J. Sci. Stat. Comput. 7, 378-417 (1986). Reviewer: M.Bartušek MSC: 65L05 65F10 34A34 PDFBibTeX XMLCite \textit{T. F. Chan} and \textit{K. R. Jackson}, SIAM J. Sci. Stat. Comput. 7, 378--417 (1986; Zbl 0611.65050) Full Text: DOI