Efficient solution of parameter‐dependent quasiseparable systems and computation of meromorphic matrix functions

Summary In this paper, we focus on the solution of shifted quasiseparable systems and of more general parameter‐dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the quasiseparable structure under diagonal shifting and inve...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2018-12, Vol.25 (6), p.n/a
Main Authors: Boito, P., Eidelman, Y., Gemignani, L.
Format: Article
Language:English
Subjects:
Algorithms
Mathematics
matrix equation
matrix function
Numerical Analysis
Parameters
QR factorization
quasiseparable matrices
Robustness (mathematics)
shifted linear system
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Summary:Summary In this paper, we focus on the solution of shifted quasiseparable systems and of more general parameter‐dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the quasiseparable structure under diagonal shifting and inversion. This algorithm is applied to compute various functions of matrices. Numerical experiments show that this approach is fast and numerically robust.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2141