Faculty of Computing and Information Science >
Center for Advance Computing >
Cornell Theory Center Technical Reports >
Please use this identifier to cite or link to this item:
|Title: ||Matrix Iterations: The Six Gaps Between Potential Theory and Convergence|
|Authors: ||Driscoll, Tobin A.|
Trefethen, Lloyd N.
|Keywords: ||theory center|
|Issue Date: ||Jun-1996|
|Publisher: ||Cornell University|
|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 rho less than 1 can be derived by solving a problem of potential theory or conformal mapping. Six approximations are involved in reducing 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.|
|Appears in Collections:||Cornell Theory Center Technical Reports|
Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.