Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Krylov subspace methods for solving large unsymmetric linear systems

Journal Article · · Math. Comput.; (United States)

Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r/sub 0/, Ar/sub 0/,...,A/sup m/-1r/sub 0/) are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi's algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace K/sub m/ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.

DOE Contract Number:
EY-76-S-02-2383
OSTI ID:
6244468
Journal Information:
Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 36:155; ISSN MCMPA
Country of Publication:
United States
Language:
English

Similar Records

Krylov subspace methods for solving large unsymmetric linear systems
Technical Report · Wed Dec 31 23:00:00 EST 1980 · OSTI ID:6560074

Diomres (k,m): An efficient method based on Krylov subspaces to solve big, dispersed, unsymmetrical linear systems
Conference · Tue Feb 28 23:00:00 EST 1995 · OSTI ID:107199

Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM
Journal Article · Wed May 20 00:00:00 EDT 2020 · SIAM Journal on Matrix Analysis and Applications · OSTI ID:1832747