A Taylor expansion of the square root matrix function

By Pierre Del Moral, Angèle Niclas. Journal of Mathematical Analysis and Applications, 2017

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Abstract This short note provides an explicit description of the Frechet derivatives of the principal square root matrix function at any order. We present an original formulation that allows to compute sequentially the Frechet derivatives of the matrix square root at any order starting from the first order derivative. A Taylor expansion at any order with an integral remainder term is also provided, yielding the first result of this type for this class of matrix function.

Subfields: Computational Theory and Mathematics, Numerical Analysis

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