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|Title:||From potential theory to matrix iterations in six steps|
|Source:||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|
|Appears in Collections:||Staff Publications|
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