Double-shift-invert Arnoldi method for computing the matrix exponential

Computing the matrix exponential for large sparse matrices is essential for solving evolution equations numerically. Conventionally, the shift-invert Arnoldi method is used to compute a matrix exponential and a vector product. This method transforms the original matrix using a shift, and generates t...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2018-07, Vol.35 (2), p.727-738
Main Authors: Hashimoto, Yuka, Nodera, Takashi
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Original Paper
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Summary:Computing the matrix exponential for large sparse matrices is essential for solving evolution equations numerically. Conventionally, the shift-invert Arnoldi method is used to compute a matrix exponential and a vector product. This method transforms the original matrix using a shift, and generates the Krylov subspace of the transformed matrix for approximation. The transformation makes the approximation converge faster. In this paper, a new method called the double-shift-invert Arnoldi method is explored. This method uses two shifts for transforming the matrix, and this transformation results in a faster convergence than the shift-invert Arnoldi method.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-018-0309-9