Matrix exponentials and inversion of confluent Vandermonde matrices.
Uwe Luther, Karla Rost · 2004
Abstract. For a given matrix A we compute the matrix exponential e tA under the assumption that the eigenvalues of A are known, but without determining the eigenvectors. The presented approach exploits the connection between matrix exponentials and confluent Vandermonde matrices V. This approach and the resulting methods are very simple and can be regarded as an alternative to the Jordan canonical form methods. The discussed inversion algorithms for V as well as the matrix representation of V −1 are of independent interest also in many other applications.