Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 38, Issue 3, Pages A1639-A1661Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1027620
Keywords
Leja interpolation; backward error analysis; action of matrix exponential; exponential integrators; phi functions; Taylor series
Categories
Funding
- DOC fellowship of the Austrian Academy of Science at the Department of Mathematics, University of Innsbruck, Austria
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The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix exponential on a given vector is a typical application. This quantity is required, e.g., in exponential integrators. The Leja method essentially depends on three parameters: the scaling parameter, the location of the interpolation points, and the degree of interpolation. We present here a backward error analysis that allows us to determine these three parameters as a function of the prescribed accuracy. Additional aspects that are required for an efficient and reliable implementation are discussed. Numerical examples illustrating the performance of our MATLAB code are included.
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