publication . Article . 2019

Biorthogonal rational Krylov subspace methods

Niel Van Buggenhout; Marc Van Barel; Raf Vandebril;
Open Access
  • Published: 05 Dec 2019
  • Publisher: Kent State University Library
  • Country: Belgium
Abstract
A general framework for oblique projections of non-Hermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can be written efficiently as a structured pencil, where the structure can take several forms such as Hessenberg or inverse Hessenberg. One specific instance of the structures appearing in this framework for oblique projections is a tridiagonal pencil. This is a direct generalization of the classical biorthogonal Krylov subspace method, where the projection becomes a single non-Hermitian tridiagonal matrix and of the Hessenberg pe...
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Subjects
arXiv: Mathematics::Numerical AnalysisComputer Science::Mathematical SoftwareComputer Science::Numerical Analysis
free text keywords: Analysis, Mathematics, Krylov subspace, Biorthogonal system, Algebra
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