Computing low‐rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods

The Fréchet derivative Lf(A,E) of the matrix function f(A) plays an important role in many different applications, including condition number estimation and network analysis. We present several different Krylov subspace methods for computing low‐rank approximations of Lf(A,E) when the direction term...

Full description

Saved in:
Bibliographic Details
Published in:Numerical linear algebra with applications Vol. 28; no. 6
Main Authors: Kandolf, Peter, Koskela, Antti, Relton, Samuel D., Schweitzer, Marcel
Format: Journal Article
Language:English
Published: Oxford Wiley Subscription Services, Inc 01.12.2021
Subjects:
Approximation
Computation
Fréchet derivative
Krylov subspace
matrix exponential
matrix function
Network analysis
Stieltjes function
Subspace methods
ISSN:1070-5325, 1099-1506
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Fréchet derivative Lf(A,E) of the matrix function f(A) plays an important role in many different applications, including condition number estimation and network analysis. We present several different Krylov subspace methods for computing low‐rank approximations of Lf(A,E) when the direction term E is of rank one (which can easily be extended to general low rank). We analyze the convergence of the resulting methods both in the Hermitian and non‐Hermitian case. In a number of numerical tests, both including matrices from benchmark collections and from real‐world applications, we demonstrate and compare the accuracy and efficiency of the proposed methods.
Bibliography:Funding information
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, 156215
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2401