## From Potential Theory To Matrix Iterations In Six Steps

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Venue: | SIAM REVIEW |

Citations: | 35 - 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.