A fixed point iteration for computing the matrix logarithm

Details A fixed point iteration for computing the matrix logarithm A fixed point iteration for computing the matrix logarithm

2007-07-18

arxiv.org/abs/0707.2701v1

Computer Science

Numerical Analysis

4 pages, 3 figures, comments welcome

Scientific paper

In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical method calculates successive square roots. In this article, a new algorithm is presented that relies on the computation of successive matrix exponentials. Convergence of the method is demonstrated for a large class of initial matrices and favorable choices of the initial matrix are discussed.

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