On the Convergence of Rational Ritz Values
نویسندگان
چکیده
منابع مشابه
On the Convergence of Rational Ritz Values
Ruhe’s rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained ext...
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FOM and GMRES are Krylov subspace iterative methods for solving nonsymmetric linear systems. The Ritz values are approximate eigenvalues, which can be computed cheaply within these algorithms. In this paper, we generalise the concept of Harmonic Ritz values, introduced by Paige et al. for symmetric matrices, to nonsymmetric matrices. We show that the zeroes of the residual polynomials of FOM an...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2010
ISSN: 0895-4798,1095-7162
DOI: 10.1137/090755412