Name
Abstract | ||
|---|---|---|
We offer a systematic study of Krylov subspace methods for solving skew-symmetric linear systems. For the method of conjugate gradients we derive a backward stable block decomposition of skew-symmetric tridiagonal matrices and set search directions that satisfy a special relationship, which we call skew-$A$-conjugacy. Imposing Galerkin conditions, the resulting scheme is equivalent to the CGNE algorithm, but the derivation does not rely on the normal equations. We also discuss minimum residual algorithms, review recent related work, and show how the iterations are derived. The important question of preconditioning is then addressed. The preconditioned iterations we develop are based on preserving the skew-symmetry, and we introduce an incomplete $2\times2$ block $LDL^T$ decomposition. A numerical example illustrates the convergence properties of the algorithms and the effectiveness of the preconditioning approach. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/080732390 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
convergence property,cgne algorithm,iterative solution,krylov subspace method,conjugate gradient,skew-symmetric linear systems,imposing galerkin condition,important question,stable block decomposition,skew-symmetric linear system,preconditioning approach,skew-symmetric tridiagonal matrix,skew symmetric,linear system | Tridiagonal matrix,Conjugate gradient method,Krylov subspace,Linear algebra,Mathematical optimization,Linear system,Matrix (mathematics),Iterative method,Numerical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
31 | 2 | 0895-4798 |
Citations | PageRank | References |
4 | 0.44 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| CHEN GREIF | 1 | 321 | 43.63 |
| James M. Varah | 2 | 91 | 24.37 |