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Title: From potential theory to matrix iterations in six steps
Authors: Driscoll, T.A.
Toh, K.-C. 
Trefethen, L.N.
Keywords: Conformal mapping
Krylov subspaces
Matrix iterations
Polynomial approximation
Potential theory
Semidefinite programming
Issue Date: Sep-1998
Citation: Driscoll, T.A.,Toh, K.-C.,Trefethen, L.N. (1998-09). From potential theory to matrix iterations in six steps. SIAM Review 40 (3) : 547-578. ScholarBank@NUS Repository.
Abstract: The theory of the convergence of Krylov subspace iterations for linear systems of equations (conjugate gradients, biconjugate gradients, GMRES, QMR, Bi-CGSTAB, and so on) is reviewed. For a computation of this kind, an estimated asymptotic convergence factor ρ ≤ 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.
Source Title: SIAM Review
ISSN: 00361445
Appears in Collections:Staff Publications

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