Name
Abstract | ||
|---|---|---|
Abstract—In this paper we introduce and analyze a new precon- ditioner for Toeplitz matrices that exhibits excellent spectral prop- erties:theeigenvaluesofthepreconditionedmatrixarehighlyclus- tered around the unity. As a result,it yields veryrapid convergence when used to solve Toeplitz equations via the preconditioned con- jugate gradient method. The new preconditioner can be regarded as a refinement of preconditioners built by embedding the Toeplitz matrix inapositivedefinite circulant.Necessaryandsufficientcon- ditions that ensure that the positive definite embedding is possible are given. Index Terms—PCG, preconditioners, Toeplitz matrices. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/LSP.2009.2024735 | IEEE Signal Process. Lett. |
Keywords | Field | DocType |
conjugate gradient methods,eigenvalues and eigenfunctions,matrix algebra,Toeplitz equations,Toeplitz matrices,eigenvalues,preconditioned conjugate gradient method,PCG,Toeplitz matrices,preconditioners | Conjugate gradient method,Mathematical optimization,Preconditioner,Matrix (mathematics),Iterative method,Positive-definite matrix,Toeplitz matrix,Circulant matrix,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
16 | 9 | 1070-9908 |
Citations | PageRank | References |
3 | 0.72 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| María Elena Domínguez-Jiménez | 1 | 4 | 2.12 |
| Paulo J. S. G. Ferreira | 2 | 137 | 25.98 |