Name
Abstract | ||
|---|---|---|
In this paper we introduce a new approach for reducing communication in Krylov subspace methods that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration, based on a domain decomposition of the graph of A. The obtained enlarged Krylov subspace K-k,K- t(A, r(0)) is a superset of the Krylov subspace K-k(A, r(0)), K-k(A, r(0)) subset of K-k,K- t(A, r(0)). Thus, we search for the solution of the system Ax = b in K-k,K- t(A, r(0)) instead of K-k(A, r(0)). Moreover, we show in this paper that the enlarged Krylov projection subspace methods lead to faster convergence in terms of iterations and parallelizable algorithms with less communication, with respect to Krylov methods. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/140989492 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
minimizing communication,linear algebra,iterative methods | Conjugate gradient method,Parallelizable manifold,Krylov subspace,Linear algebra,Discrete mathematics,Subset and superset,Mathematical optimization,Combinatorics,Subspace topology,Iterative method,Mathematics,Domain decomposition methods | Journal |
Volume | Issue | ISSN |
37 | 2 | 0895-4798 |
Citations | PageRank | References |
3 | 0.41 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laura Grigori | 1 | 368 | 34.76 |
| sophie moufawad | 2 | 3 | 0.41 |
| Frédéric Nataf | 3 | 248 | 29.13 |