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

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