A Generalization of the Kreiss Matrix Theorem.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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.
- Theoretical Mathematics