From Potential Theory To Matrix Iterations In Six Steps
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| Venue: | SIAM REVIEW |
| Citations: | 28 - 4 self |
BibTeX
@ARTICLE{Driscoll_frompotential,
author = {Tobin A. Driscoll and Kim-Chuan Toh and Lloyd N. Trefethen},
title = {From Potential Theory To Matrix Iterations In Six Steps},
journal = {SIAM REVIEW},
year = {},
volume = {40},
pages = {547--578}
}
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Abstract
The theory of the convergence of Krylov subspace iterations for linear systems of equations (conjugate gradients, biconjugate gradients, GMRES, QMR, Bi-CGSTAB, ...) is reviewed. For a computation of this kind, an estimated asymptotic convergence factor ae 1 can be derived by solving a problem of potential theory or conformal mapping. Six approximations are involved in relating the actual computation to this scalar estimate. These six approximations are discussed in a systematic way and illustrated by a sequence of examples computed with tools of numerical conformal mapping and semidefinite programming.
