## A spectral Newton-Schur algorithm for the solution of symmetric generalized eigenvalue problems

Vassilis Kalantzis

### Abstract

This paper proposes a numerical algorithm based on spectral Schur complements to compute a few eigenvalues and the associated eigenvectors of symmetric matrix pencils. The proposed scheme follows an algebraic domain decomposition viewpoint and transforms the generalized eigenvalue problem into one of computing roots of scalar functions. These scalar functions are defined so that their roots are equal to the eigenvalues of the original pencil, and these roots are computed by Newton's method. We describe the theoretical aspects of the proposed scheme and demonstrate its performance on a few test problems.

Full Text (PDF) [7.5 MB], BibTeX

### Key words

spectral Schur complements, domain decomposition, symmetric generalized eigenvalue problem, Newton's method

### AMS subject classifications

65F15, 15A18, 65F50

### Links to the cited ETNA articles

 [11] Vol. 45 (2016), pp. 305-329 Vassilis Kalantzis, Ruipeng Li, and Yousef Saad: Spectral Schur complement techniques for symmetric eigenvalue problems

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