Generalized complex step approximation to estimate the first and second order Fréchet derivative of matrix functions-Reference-Cited by-同舟云学术

Generalized complex step approximation to estimate the first and second order Fréchet derivative of matrix functions

Published:2022 Issue:16 Volume:36 Page:5603-5614
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Arslan Bahar¹,Al-Mohy Awad²

Affiliation:

1. Mathematics Department, Faculty of Engineering and Natural Sciences, Bursa Technical University, Turkey

2. Department of Mathematics, King Khalid University, Abha, Saudi Arabia

Abstract

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 approximation to the first and the second order Fr?chet derivative of the matrix exponential and matrix square root.

Publisher

National Library of Serbia

Subject

General Mathematics

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