Approximate eigenvalues, eigenvectors and inverse of a matrix with polynomial entries (Q1325135)

The author presents algorithms for approximate evaluation of eigenvalues, eigenvectors and the inverse of a given square matrix with polynomial entries. The characteristic feature of the algorithms presented in the paper is the exploitation of the truncated Taylor series. Apart from basic algorithms, the author discusses acceleration of convergence and gives error estimates. The performance of the algorithms is illustrated on examples that are worked out in detail.