The complex step approximation to the higher order Fréchet derivatives of a matrix function
type: Item
instance of: scholarly article
title: The complex step approximation to the higher order Fréchet derivatives of a matrix function
zbMATH Open document ID: 1469.65085
author: Awad H. Al-Mohy
author: Bahar Arslan
published in: Numerical Algorithms
publication date: 2021-06-24T00:00:00Z
Mathematics Subject Classification ID: 65F60
Mathematics Subject Classification ID: 15A16
zbMATH DE Number: 7363165
zbMATH Keywords: matrix function
zbMATH Keywords: Fréchet derivative
zbMATH Keywords: higher order Fréchet derivative
zbMATH Keywords: complex step approximation
zbMATH Keywords: action of matrix functions
describes a project that uses: mftoolbox
MaRDI profile type: Publication
full work available at URL: s11075-020-00998-3
OpenAlex ID: W3082404345
cites work: On the generalization of the complex step method
cites work: A Convex Optimization Approach for Computing Correlated Choice Probabilities With Many Alternatives
cites work: A Truncated Taylor Series Algorithm for Computing the Action of Trigonometric and Hyperbolic Matrix Functions
cites work: Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation
cites work: A New Scaling and Squaring Algorithm for the Matrix Exponential
cites work: The complex step approximation to the Fréchet derivative of a matrix function
cites work: Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
cites work: Computing the Fréchet derivative of the matrix logarithm and estimating the condition number
cites work: Geometric constructions of iterative functions to solve nonlinear equations
cites work: A finite element method for quantum graphs
cites work: Ranking hubs and authorities using matrix functions
cites work: Computation of the matrix \(p\)th root and its Fréchet derivative by integrals
cites work: Computing survival functions of the sum of two independent Markov processes: an application to bladder carcinoma treatment
cites work: Functions of Matrices
cites work: Computing the Action of Trigonometric and Hyperbolic Matrix Functions
cites work: An improved Schur-Padé algorithm for fractional powers of a matrix and their Fréchet derivatives
cites work: Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number
cites work: A survey and comparison of contemporary algorithms for computing the matrix geometric mean
cites work: A Block Krylov Method to Compute the Action of the Fréchet Derivative of a Matrix Function on a Vector with Applications to Condition Number Estimation
cites work: A Schur--Fréchet Algorithm for Computing the Logarithm and Exponential of a Matrix
cites work: Extensions of the first and second complex-step derivative approximations
cites work: Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
cites work: Numerical Differentiation of Analytic Functions
cites work: A Formula for the Fréchet Derivative of a Generalized Matrix Function
cites work: Using Complex Variables to Estimate Derivatives of Real Functions
DOI: 10.1007/S11075-020-00998-3
description: scientific article; zbMATH DE number 7363165