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arXiv · 2401.10089

Polynomial approximations for the matrix logarithm with computation graphs

Elias Jarlebring·Jorge Sastre·J. Javier Ibáñez González
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Abstract

The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational effort lies in matrix-matrix multiplications and left matrix division. In this work we illustrate that the number of such operations can be substantially reduced, by using a graph based representation of an efficient polynomial evaluation scheme. A technique to analyze the rounding error is proposed, and backward error analysis is adapted. We provide substantial simulations illustrating competitiveness both in terms of computation time and rounding errors.

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Elias Jarlebring, Jorge Sastre, J. Javier Ibáñez González. 2024-01-18. Polynomial approximations for the matrix logarithm with computation graphs. https://arxiv.org/abs/2401.10089

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