Recycling Krylov Subspaces for Sequences of Linear Systems

Recycling Krylov Subspaces for Sequences of Linear Systems (2004)

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Michael L. Parks , Eric De Sturler , Greg Mackey , Duane D. Johnson , Spandan Maiti

Venue:	SIAM J. Sci. Comput
Citations:	26 - 2 self

BibTeX

@TECHREPORT{Parks04recyclingkrylov,
    author = {Michael L. Parks and Eric De Sturler and Greg Mackey and Duane D. Johnson and Spandan Maiti},
    title = {Recycling Krylov Subspaces for Sequences of Linear Systems},
    institution = {SIAM J. Sci. Comput},
    year = {2004}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two dierent approaches. For several model problems, we demonstrate that we can reduce the iteration count required to solve a linear system by a factor of two. We consider both Hermitian and non-Hermitian problems, and present numerical experiments to illustrate the eects of subspace recycling.

Citations

1075	Iterative Methods for Sparse Linear Systems - Saad - 1996
1061	GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems - Saad, Schultz - 1986
147	Variational iterative methods for nonsymmetric systems of linear equations - Eisenstat, Elman, et al. - 1983
103	der Vorst: Numerical Linear Algebra for High-Performance Computing - Dongarra, Duff, et al. - 1998
83	The block conjugate gradient algorithm and related - O’Leary - 1980
65	The matrix market: A web resource for test matrix collections - Boisvert, Pozo, et al. - 1997
52	A restarted GMRES method augmented with eigenvectors - Morgan - 1995
50	Implicit parallel processing in structural mechanics - Farhat, Roux - 1994
46	An iterative method for nonsymmetric systems with multiple right hand sides - Simoncini, Gallopoulos - 1995
37	Matrix Algorithms (Volume II: Eigensystems - Stewart - 2011
33	Adaptively preconditioned GMRES algorithms - Baglama, Calvetti, et al. - 1998
33	Dynamic thick restarting of the Davidson, and the implicitly restarted arnoldi methods - Stathopoulos, Saad, et al. - 1998
30	Etude de Quelques Méthodes de Résolution de Problèmes Linéaires de Grande Taille sur Multiprocesseur - Vital - 1990
28	Truncation strategies for optimal Krylov subspace methods - Sturler - 1999
27	Restarted GMRES preconditioned by deflation - Erhel, Burrage, et al. - 1996
23	GMRES with deflated restarting - Morgan
22	Thick-restart Lanczos method for large symmetric eigenvalue problems - Wu, Simon
20	Analysis of augmented Krylov subspace methods - Saad - 1997
19	Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations - Morgan
18	Projection techniques for iterative solution of Ax = b with succesive right-hand sides - Fischer - 1997
18	Convergence of restarted Krylov subspaces to invariant subspaces - Beattie, Embree, et al.
17	Analysis of acceleration strategies for restarted minimal residual methods - Eiermann, Ernst, et al.
17	A deflated version of the conjugate gradient algorithm - Saad, Yeung, et al.
14	The superlinear convergence behaviour of - Vorst, Vuik - 1993
13	der Vorst, Numerical methods for the qcd overlap operator. i: Sign- function and error - Eshof, Frommer, et al. - 2002
11	Galerkin projection methods for solving multiple linear systems - Chan, Ng - 1999
10	Nested Krylov methods based on GCR - Sturler - 1996
10	Solution of the Schrödinger equation in periodic lattices with an application to methalic lithium, Phys. Rev. 94:1111 - Kohn, Rostoker - 1954
10	On the occurrence of superlinear convergence of exact and inexact Krylov subspace methods - Simoncini, Szyld
9	A deflated version of the conjugate gradient algorithm - SAAD, YEUNG, et al. - 1998
8	Sturler, Recycling subspace information for diffuse optical tomography - Kilmer, de
8	Nested Krylov methods based on - Sturler - 1996
8	der Vorst, Numerical methods for the QCD overlap operator: I Sign function and error bounds - Lippert, van
7	On the calculation of the energy of a Bloch wave in a metal - Korringa - 1947
5	Inner-outer methods with deflation for linear systems with multiple right-hand sides - Sturler - 1996
4	Energy and pressure calculations for random substitutional alloys - Johnson, Nicholson, et al. - 1990
4	On the reuse of Ritz vectors for the solution to nonlinear elasticity problems by domain decomposition methods - Risler, Rey - 1998
4	Accuracy and limitations of localized Green’s function methods for materials science applications - Smirnov, Johnson
4	Theory and convergence properties of the screened Korringa-Kohn-Rostoker method - Zeller, Dederichs, et al. - 1995
3	Restarted GMRES preconditioned by de - Erhel, Burrage, et al. - 1996
3	MPI-based implementation of a PCG solver using an EBE architecture and preconditioner for implicit, 3-D finite element analyses - Gullerud, Dodds
3	A Rayleigh-Ritz preconditioner for the iterative solution to large scale nonlinear problems, Numerical Algorithms - Rey, Risler - 1998
3	On the superlinear convergence of exact and inexact Krylov subspace methods - Simoncini, Szyld - 2003
3	with deflated restarting - GMRES - 2003
3	Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems - Risler, Rey
2	Reusing Krylov subspaces for sequences of linear systems - Mackey - 2003
2	Set QCD: Quantum Chromodynamics. Description of matrix set - Medeke
2	restarted GMRES and Arnoldi methods for nonsymmetric systems of equations - Implicitly
2	A new family of block methods - Yang, Gallivan - 1999
2	The Iterative Solution of a Sequence of Linear Systems Arising from Nonlinear Finite Element Analysis - Parks - 2005