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A restarted Krylov method with inexact inversions
Author(s) -
Dax Achiya
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2213
Subject(s) - eigenvalues and eigenvectors , mathematics , lanczos resampling , convergence (economics) , monotonic function , polynomial , inverse , positive definite matrix , iterative method , matrix (chemical analysis) , algorithm , mathematical optimization , mathematical analysis , physics , geometry , materials science , quantum mechanics , economics , composite material , economic growth
Summary In this paper, we present a new type of restarted Krylov method for calculating the smallest eigenvalues of a symmetric positive definite matrix G . The new framework avoids the Lanczos tridiagonalization process and the use of polynomial filtering. This simplifies the restarting mechanism and allows the introduction of several modifications. Convergence is assured by a monotonicity property that pushes the eigenvalues toward their limits. Another innovation is the use of inexact inversions of G to generate the Krylov matrices. In this approach, the inverse of G is approximated by using an iterative method to solve the related linear system. Numerical experiments illustrate the usefulness of the proposed approach.