Generalized Complex Step Approximation to Estimate the First and Second Order Frechet Derivative of Matrix Functions

Abstract

Applications of Frechet derivative emerge in the sensitivity analysis of matrix functions. Our work extends the generalized complex step approximation using the complex computation f (A + e(i theta)hE) as a tool to matrix case, and combines it with finite difference formula to estimate the Frechet derivative. We provide numerical results for the approximation to the first and the second order Frechet derivative of the matrix exponential and matrix square root.