Volume 33, pp. 17-30, 2008-2009.
Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization
M. Bellalij, Y. Saad, and H. Sadok
Abstract
Krylov subspace methods are strongly related to polynomial spaces
and their convergence analysis can often be naturally derived from
approximation theory. Analyses of this type lead to discrete min-max
approximation problems over the spectrum of the matrix, from which
upper bounds on the relative Euclidean residual norm are derived. A
second approach to analyzing the convergence rate of the GMRES
method or the Arnoldi iteration, uses as a primary indicator the
(1,1) entry of the inverse of
Full Text (PDF) [177 KB], BibTeX
Key words
Krylov subspaces, polynomials of best approximation, min-max problem, interpolation, convex optimization, KKT optimality conditions
AMS subject classifications
65F10, 65F15
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