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Simultaneous iteration methods are presented for obtaining dominanteigenvalues and corresponding eigenvectors of real unsymmetricmatrices. These methods involve the accurate eigensolution ofthe smaller interaction matrix at each iteration, the dimensionsof which depend on the number of vectors processed simultaneously.A bi-iteration procedure is proposed when both left and righteigenvectors are required, and a lopsided iteration procedurewhen only one set of eigenvectors is required. Numerical testsare discussed. 相似文献
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New perturbation analyses for the Cholesky factorization 总被引:1,自引:0,他引:1
CHANG XIAO-WEN; PAIGE CHRISTOPHER C.; STEWART G. W. 《IMA Journal of Numerical Analysis》1996,16(4):457-484
We present new perturbation analyses for the Cholesky factorizationA = RT R of a symmetric positive definite matrix A. The analysesmore accurately reflect the sensitivity of the problem thanprevious normwise results. The condition numbers here are alteredby any symmetric pivoting used in PAPT = RTR, and both numericalresults and an analysis show that the standard method of pivotingis optimal in that it usually leads to a condition number veryclose to its lower limit for any given A. It follows that thecomputed R will probably have greatest accuracy when we usethe standard symmetric pivoting strategy. Initially we give a thorogh analysis to obtain both first-orderand strict normwise perturbation bounds which are as tight aspossible, leading to a definition of an optimal condition numberfor the problem. Then we use this approach to obtain reasonablyclear first-order and strict componentwise perturbation bounds. We complete the work by giving a much simpler normwise analysiswhich provides a somewhat weaker bound, but which allows usto estimate the condition of the problem quite well with anefficient computation. This simpler analysis also shows whythe factorization is often less sensitive than we previouslythought, and adds further insight into why pivoting usuallygives such good results. We derive a useful upper bound on thecondition of the problem when we use pivoting.
This research was supported by the Natural Sciences and EngineeringResearch Ciuncil of Canada Grant OGP0009236.
This research was supported in part by the US National ScienceFoundation under grant CCR 95503126. 相似文献
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Bruins EE Bauer TS den Bok HW Duif CP van Hoek WC de Lange DJ Misiejuk A Papandreou Z Sichtermann EP Tjon JA Willering HW Yeomans DM Reike H Durek D Frommberger F Gothe R Jakob D Kranefeld G Kunz C Leiendecker N Pfeiffer G Putsch H Reichelt T Schoch B Wacker D Wehrmeister D Wilhelm M Jans E Konijn J de Vries R Furget C Voutier E Arenhövel H 《Physical review letters》1995,75(1):21-24
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