Controlled Markov chains, graphs, and Hamiltonicity
Foundations and Trends® in Stochastic Systems
Journal of Computational and Applied Mathematics
A local construction of the Smith normal form of a matrix polynomial
Journal of Symbolic Computation
Hi-index | 0.00 |
In this paper we study the inversion of an analytic matrix valued function A(z). This problem can also be viewed as an analytic perturbation of the matrix A0=A(0). We are mainly interested in the case where A0 is singular but A(z) has an inverse in some punctured disc around z=0. It is known that A-1(z) can be expanded as a Laurent series at the origin. The main purpose of this paper is to provide efficient computational procedures for the coefficients of this series. We demonstrate that the proposed algorithms are computationally superior to symbolic algebra when the order of the pole is small.