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Computing a partial generalized real Schur form using the Jacobi–Davidson method
Author(s) -
Noorden Tycho van,
Rommes Joost
Publication year - 2007
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.523
Subject(s) - mathematics , eigenvalues and eigenvectors , pencil (optics) , complex conjugate , jacobi method , krylov subspace , invariant subspace , subspace topology , invariant (physics) , conjugate gradient method , matrix pencil , convergence (economics) , algorithm , pure mathematics , mathematical analysis , iterative method , linear subspace , mechanical engineering , physics , quantum mechanics , engineering , economics , mathematical physics , economic growth
In this paper, a new variant of the Jacobi–Davidson (JD) method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugate pair of eigenvalues, the method computes the two‐dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. Both real and complex formulations of the correction equation are considered. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method. Copyright © 2007 John Wiley & Sons, Ltd.