Approximate eigenvalues, eigenvectors and inverse of a matrix with polynomial entries

Abstract

LetM be a matrix with polynomial entries. This paper deals with calculating eigenvalues, eigenvectors and inverse ofM approximately in the form of truncated power series. The calculation of approximate eigenvalues is based on algorithms solving algebraic equation symbolically in terms of power series. Then, we give algorithms for calculating eigenvectors and inverse in terms of power series approximately. We show an example for each algorithm. Finally, we explain acceleration of convergence of power series and estimate of errors due to truncation of power series.