A truncated-CG style method for symmetric generalized eigenvalue problems

Absil, Pierre-Antoine;Baker, CG;Gallivan, KA
(2006) Journal of Computational and Applied Mathematics —

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A numerical algorithm is proposed for computing an extreme eigenpair of a symmetric/positive-definite matrix pencil (A, B). The leftmost or the rightmost eigenvalue can be targeted. Knowledge of (A, B) is only required through a routine that performs matrix-vector products. The method has excellent global convergence properties and its local rate of convergence is superlinear. It is based on a constrained truncated-CG trust-region strategy to optimize the Rayleigh quotient, in the framework of a recently proposed trust-region scheme on Riemannian manifolds. (c) 2005 Elsevier B.V. All rights reserved.
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Absil, P.-A., Baker, C., & Gallivan, K. (2006). A truncated-CG style method for symmetric generalized eigenvalue problems. Journal of Computational and Applied Mathematics. https://hdl.handle.net/2078.5/140190