On the Numerical Stability of the Rayleigh–Ritz Method

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1977 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 14, pages 1,151-1,171 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Omodei, Bernard J.;

doi: 10.1137/0714080

On the Numerical Stability of the Rayleigh–Ritz Method

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Abstract

The numerical stability of the Rayleigh–Ritz method is investigated from the point of view of Mikhlin stability and of the condition number of the Rayleigh–Ritz matrix, and it is shown that the condition number approach is more appropriate for floating-point computation. An a priori and an a posteriori strategy for practical stability control are introduced, and illustrated with numerical examples.

Keywords

Numerical solution of boundary value problems involving ordinary differential equations, General theory of numerical analysis in abstract spaces

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