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In various areas of applied numerics, the problem of calculating thelogarithm of a matrix A emerges. Since series expansions of the logarithmusually do not converge well for matrices far away from the identity, thestandard numerical method calculates successive square roots. In this article,a new algorithm is presented that relies on the computation of successivematrix exponentials. Convergence of the method is demonstrated for a largeclass of initial matrices and favorable choices of the initial matrix arediscussed.

A fixed point iteration for computing the matrix logarithm