English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Applications such as the modal analysis of structures and acoustic cavities require a number of eigenvalues and eigenvectors of large scale Hermitian eigenvalue problems. The most popular method is probably the spectral transformation Lanczos method. An important disadvantage of this method is that a change of pole requires a complete restart. In this paper, we investigate the use of the rational Krylov method for this application. This method does not require a complete restart after a change of pole. The contribution of this paper is threefold. First, it is shown that the change of pole can be considered as a change of Lanczos basis. Second, moving the pole near a locked eigenvalue may prevent other eigenvalues to be computed accurately. Third, we show that a pole chosen close to an eigenvalue may lead to a loss of numerical stability. Usually, this will not lead to disaster but reduce the accuracy of the computed eigenvalues away from the pole. Numerical examples illustrate the theory.

Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem