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Full-Text Articles in Condensed Matter Physics
Recycling Krylov Subspaces For Sequences Of Linear Systems, Michael L. Parks, Eric De Sturler, Greg Mackey, Duane D. Johnson, Spandan Maiti
Recycling Krylov Subspaces For Sequences Of Linear Systems, Michael L. Parks, Eric De Sturler, Greg Mackey, Duane D. Johnson, Spandan Maiti
Duane D. Johnson
Many problems in science and engineering require the solution of a long sequence of slowly changing linear systems. We propose and analyze two methods that significantly reduce the total number of matrix‐vector products required to solve all systems. We consider the general case where both the matrix and right‐hand side change, and we make no assumptions regarding the change in the right‐hand sides. Furthermore, we consider general nonsingular matrices, and we do not assume that all matrices are pairwise close or that the sequence of matrices converges to a particular matrix. Our methods work well under these general assumptions, and …