An extension of the Kreiss stability theorem to families of matrices of unbounded order |
| |
Authors: | Michael R Gorelick Herbert C Kranzer |
| |
Institution: | Queens College, City University of New York USA;Adelphi University Garden City, New York 11530 USA |
| |
Abstract: | The Kreiss matrix theorem asserts three necessary and sufficient conditions for a family of matrices of fixed finite order to be L2-stable: a resolvent condition (R), a triangularization condition (S) and a Hermitian norm condition (H). We extend the Kreiss theorem to families of matrices of finite but unbounded order with the restriction that the degrees of the minimal polynomials of all matrices in the family are less than a fixed constant. For such matrix families, we show that (R) and (H) remain necessary and sufficient for L2-stability, while (S) must be replaced by a somewhat stronger “block triangularization” condition (S′). This extended Kreiss theorem permits a corresponding extension of the Buchanan stability theorem. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |