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...
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| Published in: | Numerical linear algebra with applications Vol. 28; no. 6 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.12.2021
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| ISSN: | 1070-5325, 1099-1506 |
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| Abstract | 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. |
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| AbstractList | 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. The Fréchet derivative of the matrix function 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 when the direction term 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. |
| Author | Schweitzer, Marcel Kandolf, Peter Koskela, Antti Relton, Samuel D. |
| Author_xml | – sequence: 1 givenname: Peter surname: Kandolf fullname: Kandolf, Peter organization: Universität Innsbruck – sequence: 2 givenname: Antti surname: Koskela fullname: Koskela, Antti organization: University of Helsinki – sequence: 3 givenname: Samuel D. surname: Relton fullname: Relton, Samuel D. organization: The University of Leeds – sequence: 4 givenname: Marcel orcidid: 0000-0002-4937-2855 surname: Schweitzer fullname: Schweitzer, Marcel email: marcel.schweitzer@hhu.de organization: Heinrich‐Heine‐Universität Düsseldorf |
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| Snippet | 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... The Fréchet derivative of the matrix function plays an important role in many different applications, including condition number estimation and network... |
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| SubjectTerms | Approximation Computation Fréchet derivative Krylov subspace matrix exponential matrix function Network analysis Stieltjes function Subspace methods |
| Title | Computing low‐rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods |
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