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arXiv · 1506.08665

The Leja method revisited: backward error analysis for the matrix exponential

Marco Caliari·Peter Kandolf·Alexander Ostermann·Stefan Rainer
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Abstract

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 that illustrate the performance of our Matlab code are included.

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Marco Caliari, Peter Kandolf, Alexander Ostermann, Stefan Rainer. 2015-06-29. The Leja method revisited: backward error analysis for the matrix exponential. https://doi.org/10.1137/15m1027620

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