Another Dubious Way to Compute the Exponential of a Matrix

Abstract

In this paper we analyzed recent works on inverting Vandermonde matrix, both classical and generalized, which were unknown during the publication of Moler’s and Van Loan’s paper ‘Nineteen Dubious Ways to Compute the Exponential of a Matrix’. Upon that analysis we proposed the Vandermonde method as the fourth candidate for calculating exponent of generic matrices. On this basis we also proposed the Vandermonde based method to compute the exponential of certain class of special matrices, i.e. the companion matrices.