Analysis of a Fast Eigenvalue Algorithm for Hankel Matri es

A Fast Eigenvalue Algorithm for Hankel Matri es

A Fast Singular Value Algorithm for Hankel Matri esFranklin

Analysis of a Fast Hankel Eigenvalue Algorithm

This paper analyzes the important steps of an O(n 2 log n) algorithm for nding the eigenvalues of a complex Hankel matrix. The three key steps are a Lanczos-type tridiagonalization algorithm, a fast FFT-based Hankel matrix-vector product procedure, and a QR eigenvalue method based on complex-orthogonal transformations. In this paper, we present an error analysis of the three steps, as well as r...

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Tagungsberi ht Nr. 45 / 2000 Ni htnegative Matrizen, M-Matrizen und deren Verallgemeinerungen 26. November { 02. Dezember 2000 The onferen e was organized by D. Hershkowitz (Haifa), V. Mehrmann (Berlin) and H. S hneider (Madison). The topi s of the onferen e were the theory and appli ations of nonnegative matri es, M-matri es and their generalizations. There were 31 plenary talks and informal r...

Fast and Accurate Con-Eigenvalue Algorithm for Optimal Rational Approximations

Abstra t. The need to ompute small on-eigenvalues and the asso iated on-eigenve tors of positive-de nite Cau hy matri es naturally arises when onstru ting rational approximations with a (near) optimally small L error. Spe i ally, given a rational fun tion with n poles in the unit disk, a rational approximation with m ≪ n poles in the unit disk may be obtained from the mth on-eigenve tor of an n...