Accelerating the LSTRS Algorithm | Zendy

Jörg Lampe | Zendy; M. Rojas | Zendy; D. C. Sorensen | Zendy; Heinrich Voß | Zendy

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Accelerating the LSTRS Algorithm

Author(s) -

Jörg Lampe,

M. Rojas,

D. C. Sorensen,

Heinrich Voß

Publication year - 2011

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/090764426

Subject(s) - hessian matrix , eigenvalues and eigenvectors , mathematics , divide and conquer eigenvalue algorithm , inverse iteration , arnoldi iteration , software , algorithm , matrix (chemical analysis) , nonlinear system , convergence (economics) , iterative method , mathematical optimization , power iteration , computer science , physics , materials science , quantum mechanics , economics , composite material , programming language , economic growth

The LSTRS software for the efficient solution of the large-scale trust-region subproblem was proposed in [M. Rojas, S. A. Santos, and D. C. Sorensen, ACM Trans. Math. Software, 34 (2008), article 11]. The LSTRS method is based on recasting the problem in terms of a parameter-dependent eigenvalue problem and adjusting the parameter iteratively. The essential work at each iteration is the solution of an eigenvalue problem for the smallest eigenvalue of a bordered Hessian matrix (or two smallest eigenvalues in the potential hard case) and associated eigenvector(s). Using the nonlinear Arnoldi method to solve the eigenvalue problems makes it possible to recycle most of the information from previous iterations which can substantially accelerate LSTRS

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