Silbermann, Bernd : How to compute the partial indices of a regular and smooth matrix-valued function?

Author(s):

Silbermann, Bernd

Title:

How to compute the partial indices of a regular and smooth matrix-valued function?

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 5, 2002

Mathematics Subject Classification:

45E10			[ Integral equations of the convolution type ]
65F20			[ Overdetermined systems, pseudoinverses ]

Abstract:

This paper is aimed at the stable computation of the particial indices of regular and smooth matrix functions defined on the complex unit circle under special emphasis on the speed of convergence. A crucial role plays the k-splitting property of appropriately constructed block matrices, namely modified finite sections A_n of Toeplitz operators. It is proved that the singular values s_k(A_n) tend with high speed to zero as n \rightarrow \infty for smooth regular functions where k stands for the splitting number.

Keywords:

partial indices, Toeplitz operators, singular values

Language:

English

Publication time:

8 / 2002