The solution of parametrized symmetric linear systems

The solution of parametrized symmetric linear systems

We compare the Lanczos and MINRES methods for the solution of symmetric linear systems with a linear parameter arising from structural engineering. We show a connection with the Pade-via-Lanczos method. We propose an error estimation for the solution in finite precision arithmetic. The use of reorth...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2003, Vol.24 (4), p.1038-1059
1. Verfasser: MEERBERGEN, Karl
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Eigenvalues
Engineering
Exact sciences and technology
Fourier transforms
Iterative methods
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Beschreibung
Zusammenfassung:We compare the Lanczos and MINRES methods for the solution of symmetric linear systems with a linear parameter arising from structural engineering. We show a connection with the Pade-via-Lanczos method. We propose an error estimation for the solution in finite precision arithmetic. The use of reorthogonalization is discussed and practical algorithms are given. The theory is illustrated with numerical examples.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479800380386