Krylov subspace recycling for sequences of shifted linear systems

Applied Numerical Mathematics - Tập 81 - Trang 105-118 - 2014
Kirk M. Soodhalter1, Daniel B. Szyld2, Fei Xue3
1Industrial Mathematics Institute, Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz, Austria
2Department of Mathematics, Temple University, 1805 N Broad Street, Philadelphia, PA 19122-6094, United States
3Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States

Tài liệu tham khảo

Adbel-Rehim, 2008, Seed methods for linear equations in lattice QCD problems with multiple right-hand sides Ahmad, 2012 Baker, 2005, A technique for accelerating the convergence of restarted GMRES, SIAM J. Matrix Anal. Appl., 26, 962, 10.1137/S0895479803422014 Campbell, 1996, GMRES and the minimal polynomial, BIT Numer. Math., 36, 664, 10.1007/BF01733786 Celis, 1985, A trust region strategy for nonlinear equality constrained optimization, 71 Chan, 1997, Analysis of projection methods for solving linear systems with multiple right-hand sides, SIAM J. Sci. Comput., 18, 1698, 10.1137/S1064827594273067 Darnell, 2008, Deflated GMRES for systems with multiple shifts and multiple right-hand sides, Linear Algebra Appl., 429, 2415, 10.1016/j.laa.2008.04.019 Davis, 2011, The University of Florida sparse matrix collection, ACM Trans. Math. Softw., 38, 1:1, 10.1145/2049662.2049663 Eiermann, 2000, Analysis of acceleration strategies for restarted minimal residual methods, J. Comput. Appl. Math., 123, 261, 10.1016/S0377-0427(00)00398-8 Frommer, 2003, BiCGStab(l) for families of shifted linear systems, Computing, 70, 87, 10.1007/s00607-003-1472-6 Frommer, 1998, Restarted GMRES for shifted linear systems, SIAM J. Sci. Comput., 19, 15, 10.1137/S1064827596304563 Frommer, 1999, Fast CG-based methods for Tikhonov–Phillips regularization, SIAM J. Sci. Comput., 20, 1831, 10.1137/S1064827596313310 Frommer, 1995, Many masses on one stroke: economic computation of quark propagators, Int. J. Mod. Phys. C, 6, 627, 10.1142/S0129183195000538 Hansen, 2010 Jegerlehner, 1996 Kilmer, 2006, Recycling subspace information for diffuse optical tomography, SIAM J. Sci. Comput., 27, 2140, 10.1137/040610271 Kirchner, 2011 B. Leder, N. Bozovic, 2012, Personal communication. Lehoucq, 1996, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17, 789, 10.1137/S0895479895281484 Meerbergen, 2003, The solution of parametrized symmetric linear systems, SIAM J. Matrix Anal. Appl., 24, 1038, 10.1137/S0895479800380386 Morgan, 2000, Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations, SIAM J. Matrix Anal. Appl., 21, 1112, 10.1137/S0895479897321362 Morgan, 2002, GMRES with deflated restarting, SIAM J. Sci. Comput., 24, 20, 10.1137/S1064827599364659 Parks, 2006, Recycling Krylov subspaces for sequences of linear systems, SIAM J. Sci. Comput., 28, 1651, 10.1137/040607277 Saad, 1997, Analysis of augmented Krylov subspace methods, SIAM J. Matrix Anal. Appl., 18, 435, 10.1137/S0895479895294289 Saad, 2003 Saad, 1986, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 856, 10.1137/0907058 Simoncini, 2003, Restarted full orthogonalization method for shifted linear systems, BIT Numer. Math., 43, 459, 10.1023/A:1026000105893 Simoncini, 2005, On the occurrence of superlinear convergence of exact and inexact Krylov subspace methods, SIAM Rev., 47, 247, 10.1137/S0036144503424439 Simoncini, 2007, Recent computational developments in Krylov subspace methods for linear systems, Numer. Linear Algebra Appl., 14, 1, 10.1002/nla.499 Simoncini, 2010, Interpreting IDR as a Petrov–Galerkin method, SIAM J. Sci. Comput., 32, 1898, 10.1137/090774756 Smith, 1989, A conjugate gradient algorithm for treatment of multiple incident electromagnetic fields, IEEE Trans. Antennas Propag., 37, 1490, 10.1109/8.43571 Sonneveld, 2008, IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations, SIAM J. Sci. Comput., 31, 1035, 10.1137/070685804 Soodhalter Stathopoulos, 2010, Computing and deflating eigenvalues while solving multiple right-hand side linear systems with an application to quantum chromodynamics, SIAM J. Sci. Comput., 32, 439, 10.1137/080725532 de Sturler, 1996, Nested Krylov methods based on GCR, J. Comput. Appl. Math., 67, 15, 10.1016/0377-0427(94)00123-5 de Sturler, 1999, Truncation strategies for optimal Krylov subspace methods, SIAM J. Numer. Anal., 36, 864, 10.1137/S0036142997315950 de Sturler, 2011, Convergence bounds for approximate invariant subspace recycling for sequences of linear systems, 51 van der Vorst, 1993, The superlinear convergence behaviour of GMRES, J. Comput. Appl. Math., 48, 327, 10.1016/0377-0427(93)90028-A Wu, 2012, A preconditioned and shifted GMRES algorithm for the PageRank problem with multiple damping factors, SIAM J. Sci. Comput., 34, A2558, 10.1137/110834585