Bahar Arslan

Bursa Technical University

Applications of Fr?chet derivative emerge in the sensitivity analysis of matrix functions. Our work extends the generalized complex step approximation using the complex computation f (A + ei?hE) as a tool to matrix case, and combines it with finite difference formula to estimate the Fr?chet derivative. We provide numerical results for the approxima...

The current algorithms use either the full form or the Schur decomposition of the matrix in the inverse scaling and squaring method to compute the matrix logarithm. The inverse scaling and squaring method consists of two main calculations: taking a square root and evaluating the Padé approximants. In this work, we suggest using the structure preser...

The k th Fréchet derivative of a matrix function f is a multilinear operator from a cartesian product of k subsets of the space \(\mathbb {C}^{n\times n}\) into itself. We show that the k th Fréchet derivative of a real-valued matrix function f at a real matrix A in real direction matrices E1, E2, \(\dots \), Ek can be computed using the complex st...

We study the structured condition number of differentiable maps between smooth matrix manifolds, developing a theoretical framework that extends previous results for vector sub-spaces to any smooth manifold. We present algorithms to compute the structured condition number. As special cases of smooth manifolds, we analyze automorphism groups, and Li...