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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Given the $n\times n$ matrix polynomial $P(x)=\sum_{i=0}^kP_i x^i$, weconsider the associated polynomial eigenvalue problem. This problem, viewed interms of computing the roots of the scalar polynomial $\det P(x)$, is treatedin polynomial form rather than in matrix form by means of the Ehrlich-Aberthiteration. The main computational issues are discussed, namely, the choice ofthe starting approximations needed to start the Ehrlich-Aberth iteration, thecomputation of the Newton correction, the halting criterion, and the treatmentof eigenvalues at infinity. We arrive at an effective implementation whichprovides more accurate approximations to the eigenvalues with respect to themethods based on the QZ algorithm. The case of polynomials having specialstructures, like palindromic, Hamiltonian, symplectic, etc., where theeigenvalues have special symmetries in the complex plane, is considered. Ageneral way to adapt the Ehrlich-Aberth iteration to structured matrixpolynomial is introduced. Numerical experiments which confirm the effectivenessof this approach are reported.

Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method