publication . Article . Other literature type . 1997

On Krylov Subspace Approximations to the Matrix Exponential Operator

Marlis Hochbruck; Christian Lubich;
Open Access English
  • Published: 01 Oct 1997
  • Publisher: Society for Industrial and Applied Mathematics
  • Country: Germany
Abstract
Krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper. We derive error bounds via a functional calculus of Arnoldi and Lanczos methods that reduces the study of Krylov subspace approximations of functions of matrices to that of linear systems of equations. As a side result, we obtain error bounds for Galerkin-type Krylov methods for linear equations, namely, the biconjugate gradient method and the full orthogonalization method. For Krylov approximations to matrix exponentials, we show superlinear error decay from relatively small iteration numbers onwards, depending on the geometry of the numerical range, the spec...
Subjects
arXiv: Mathematics::Numerical AnalysisComputer Science::Numerical Analysis
free text keywords: Mathematics, ddc:510, Matrix (mathematics), Krylov subspace, Biconjugate gradient method, Mathematical analysis, Conjugate residual method, Generalized minimal residual method, Exponential integrator, Iterative method, Biconjugate gradient stabilized method
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