Computing the Inverse Matrix Hyperbolic Sine
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Computing the square root and logarithm of real P-orthogonal matrix
Applied Numerical Mathematics
Padé and Gregory error estimates for the logarithm of block triangular matrices
Applied Numerical Mathematics
Padé and Gregory error estimates for the logarithm of block triangular matrices
Applied Numerical Mathematics
Learning averages over the lie group of unitary matrices
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
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In this work, we consider computing the real logarithm of a real matrix. We pay attention to general conditioning issues, provide careful implementation for several techniques including scaling issues, and finally test and compare the techniques on a number of problems. All things considered, our recommendation for a general purpose method goes to the Schur decomposition approach with eigenvalue grouping, followed by square roots and diagonal Padé approximants of the diagonal blocks. Nonetheless, in some cases, a well-implemented series expansion technique outperformed the other methods. We have also analyzed and implemented a novel method to estimate the Frechét derivative of the $\log$, which proved very successful for condition estimation.