Luther, Uwe ; Rost, Karla : Matrix Exponentials and Inversion of Confluent Vandermonde Matrices

Author(s):

Luther, Uwe
Rost, Karla

Title:

Matrix Exponentials and Inversion of Confluent Vandermonde Matrices

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 9, 2003

Mathematics Subject Classification:

34A30			[ Linear equations and systems, general ]
65F05			[ Direct methods for linear systems and matrix inversion ]
15A09			[ Matrix inversion, generalized inverses ]
15A23			[ Factorization of matrices ]

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.

Keywords:

Matrix exponential, Vandermonde matrix, Fast algorithm, Inverse

Language:

English

Publication time:

10 / 2003