Accession Number:

ADA093569

Title:

A Generalization of the Kreiss Matrix Theorem.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1980-08-01

Pagination or Media Count:

15.0

Abstract:

In the early sixties H. O. Kreiss, while studying stability of numerical schemes for partial differential equations, considered a generalization of a problem. Namely, given a set A of n x n complex valued matrices, when all powers of A epsilon A are uniformly bounded. These sets - called the stable sets - were completely characterized by Kreiss by giving three equivalent conditions. In this paper we consider alpha-stable sets A alpha greater than 0, such that for any A epsilon A the powers A to the Nu power are uniformly bounded by K nu to the alpha power. We generalize the Kreiss resolvent condition for alpha-stable sets. It seems that alpha-stable sets are related to the concept of weakly stable numerical schemes for partial differential equations.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE