A Taylor expansion of the square root matrix functional
Provides a theoretical tool for matrix analysis, but is incremental as it extends known derivative formulas to arbitrary order.
The paper derives explicit Fréchet derivatives of the principal square root matrix functional at any order and provides a Taylor expansion with integral remainder, the first such result for this functional.
This short note provides an explicit description of the Fréchet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fréchet 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 functional.