COMPUTATIONAL TECHNIQUES FOR REAL LOGARITHMS OF MATRICES

In this work, we consider computing the real logarithm of a real matri x. We pay attention to general conditioning issues, provide careful im plementation for several techniques including scaling issues, and fina lly test and compare the techniques on a number of problems. All thing s considered, our recommendation for a general purpose method goes to the Schur decomposition approach with eigenvalue grouping, followed by square roots and diagonal Pade approximants of the diagonal blocks. N onetheless, in some cases, a well-implemented series expansion techniq ue outperformed the other methods. We have also analyzed and implement ed a novel method to estimate the Frechet derivative of the log, which proved very successful for condition estimation.