Geodesic
Matrix exponentials and inversion of confluent Vandermonde matrices
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 91-100
For a given matrix A we compute the matrix exponential etA 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.
Classification : 34A30, 65F05, 15A09, 15A23
Keywords: matrix exponential, vandermonde matrix, fast algorithm, inverse 
@article{ETNA_2004__18__a6,
     author = {Luther,  Uwe and Rost,  Karla},
     title = {Matrix exponentials and inversion of confluent {Vandermonde} matrices},
     journal = {Electronic transactions on numerical analysis},
     pages = {91--100},
     year = {2004},
     volume = {18},
     zbl = {1065.34001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a6/}
}
TY  - JOUR
AU  - Luther,  Uwe
AU  - Rost,  Karla
TI  - Matrix exponentials and inversion of confluent Vandermonde matrices
JO  - Electronic transactions on numerical analysis
PY  - 2004
SP  - 91
EP  - 100
VL  - 18
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__18__a6/
LA  - en
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%0 Journal Article
%A Luther,  Uwe
%A Rost,  Karla
%T Matrix exponentials and inversion of confluent Vandermonde matrices
%J Electronic transactions on numerical analysis
%D 2004
%P 91-100
%V 18
%U http://geodesic.mathdoc.fr/item/ETNA_2004__18__a6/
%G en
%F ETNA_2004__18__a6
Luther,  Uwe; Rost,  Karla. Matrix exponentials and inversion of confluent Vandermonde matrices. Electronic transactions on numerical analysis, Tome 18 (2004), pp. 91-100. http://geodesic.mathdoc.fr/item/ETNA_2004__18__a6/