On the Method of Partial Fractions with Matrix Coefficients and Applications

TL;DR

This paper presents a novel partial fractions method with matrix coefficients, enabling improved techniques for finding generalized eigenvectors, evaluating matrix exponentials, and solving linear ODE systems with constant coefficients.

Contribution

It introduces a new partial fractions approach with matrix coefficients and demonstrates its applications in eigenvector chains, matrix exponential evaluation, and linear differential equations.

Findings

Enhanced methods for computing chains of generalized eigenvectors

Efficient evaluation of matrix exponentials

Improved solutions for linear systems of ODEs

Abstract

The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential equations with constant coefficients.