Conditioning and Padé Approximation of the Logarithm of a Matrix

Abstract

In this work we (i) use the theory of piecewise analytic functions to represent the Fréchet derivative of any primary matrix function, in particular of primary logarithms; (ii) propose an indicator to assess inherent difficulties to compute a logarithm; and (iii) revisit Padé approximation techniques for the principal logarithm of block triangular matrices.