Foundations of Eigenvalue Distribution Theory for General & Nonnegative Matrices, Stability Criteria for Hyperbolic Initial-Boundary Value Problems, Exact Eigenvalue Computations on the ILLIAC IV

摘要

This document summarizes 46 research papers which have either appeared or will appear in major referred publications. Highlights of some of the results include: (1) Convenient stability criteria for difference approximations to hyperbolic initial boundary value problems have been obtained. The new criteria are given in terms of the boundary conditions and are independent of the basic scheme. (2) The known stability condition for the multi-dimensional Lax-Wendroff scheme has been improved. (3) Norm properties of C-numerical radii were studied. In particular, multiplicativity factors were obtained for the case where C is a normal matrix. Also, the following computer codes written for the ILLIAC IV were completed: (1) a program to determine the rank and a maximal nonvanishing subdeterminant of an integral m X n matrix; (2) a program to determine the null space of an integral m X n matrix; and (3) a program to determine all the rational solutions of an arbitrary integral linear system of equations. (Author)