Title: Computing approximate (symmetric block) rational Krylov subspaces without explicit inversion
Authors: Mach, Thomas
Pranić, Miroslav S.
Vandebril, Raf
Issue Date: Sep-2013
Publisher: Department of Computer Science, KU Leuven
Series Title: TW Reports vol:TW636
Abstract: It has been shown, see TW623, that approximate extended Krylov subspaces can be computed —under certain assumptions— without any explicit inversion or system solves. Instead the necessary products A-1v are obtained in an implicit way retrieved from an enlarged Krylov subspace. In this paper this approach is generalized to rational Krylov subspaces, which contain besides poles at infinite and zero also finite non-zero poles.

Also an adaption of the algorithm to the block and the symmetric case is presented. For all variants of the algorithm numerical experiments underpin the power of the new approach. Rational Krylov subspaces can be used, e.g., to approximate matrix functions or the solutions of matrix equations.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Numerical Analysis and Applied Mathematics Section

Files in This Item:
File Description Status SizeFormat
TW636.pdfDocument Published 1568KbAdobe PDFView/Open


All items in Lirias are protected by copyright, with all rights reserved.