A Generalization of the Kreiss Matrix Theorem.

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.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1980
Accession Number
ADA093569

Entities

People

  • Shmuel Friedland

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Banach Space
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Power Series
  • Real Variables
  • Standards
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra