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Exploiting Mixed Precision for Computing Eigenvalues of Symmetric Matrices and Singular Values
Author(s) -
Drygalla Volker
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810809
Subject(s) - eigenvalues and eigenvectors , preconditioner , singular value , singular value decomposition , mathematics , positive definite matrix , matrix (chemical analysis) , computation , symmetric matrix , eigendecomposition of a matrix , pure mathematics , mathematical analysis , algorithm , linear system , chemistry , physics , quantum mechanics , chromatography
The use of higher precision preconditioning for the symmetric eigenvalue problem and the singular value problem of general non–structured non–graded matrices are discussed. The matrix Q from the QR –decomposition as a preconditioner, applied to A with higher precision, in combination with Jacobi's method seems to allow the computation of all eigenvalues of symmetric positive definite matrices rsp. all singular values of general matrices to nearly full accuracy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)