Subspace Gap Residuals for Rayleigh–Ritz Approximations

Subspace Gap Residuals for Rayleigh–Ritz Approximations

Large-scale eigenvalue and singular value computations are usually based on extracting information from a compression of the matrix to suitably chosen low dimensional subspaces. This paper introduces new a posteriori relative error bounds based on a residual expressed using the largest principal ang...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2009-01, Vol.31 (1), p.54-67
Hauptverfasser: Bosner, Nela, Drmac, Zlatko
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Compressing
Computation
Eigenvalues
Eigenvectors
Errors
Gaps
Matrix
Studies
Subspaces
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Zusammenfassung:Large-scale eigenvalue and singular value computations are usually based on extracting information from a compression of the matrix to suitably chosen low dimensional subspaces. This paper introduces new a posteriori relative error bounds based on a residual expressed using the largest principal angle (gap) between relevant subspaces. The eigenvector approximations are estimated using subspace gaps and relative separation of the eigenvalues. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/070689425