Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

J. Alahmadi; H. Alqahtani; M. S. Pranić; L. Reichel

doi:10.1007/s11075-021-01101-0

Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

J. Alahmadi
, H. Alqahtani
, M. S. Pranić
, L. Reichel

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is concerned with the approximation of matrix functionals of the form w^Tf(A)v, where A∈ ℝⁿ^×ⁿ is a large nonsymmetric matrix, w, v∈ ℝⁿ, and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.

Original language	English
Pages (from-to)	1937-1964
Number of pages	28
Journal	Numerical Algorithms
Volume	88
Issue number	4
DOIs	https://doi.org/10.1007/s11075-021-01101-0
State	Published - Dec 2021
Externally published	Yes

Keywords

Anti-Gauss–Laurent quadrature
Extended Krylov subspace
Gauss–Laurent quadrature
Matrix function evaluation
Orthogonal Laurent polynomial

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10.1007/s11075-021-01101-0

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title = "Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix",

abstract = "This paper is concerned with the approximation of matrix functionals of the form wTf(A)v, where A∈ ℝn×n is a large nonsymmetric matrix, w, v∈ ℝn, and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.",

keywords = "Anti-Gauss–Laurent quadrature, Extended Krylov subspace, Gauss–Laurent quadrature, Matrix function evaluation, Orthogonal Laurent polynomial",

author = "J. Alahmadi and H. Alqahtani and Prani{\'c}, \{M. S.\} and L. Reichel",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Alahmadi, J.

AU - Alqahtani, H.

AU - Pranić, M. S.

AU - Reichel, L.

PY - 2021/12

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AB - This paper is concerned with the approximation of matrix functionals of the form wTf(A)v, where A∈ ℝn×n is a large nonsymmetric matrix, w, v∈ ℝn, and f is a function such that f(A) is well defined. We derive Gauss–Laurent quadrature rules for the approximation of these functionals, and also develop associated anti-Gauss–Laurent quadrature rules that allow us to estimate the quadrature error of the Gauss–Laurent rule. Computed examples illustrate the performance of the quadrature rules described.

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KW - Extended Krylov subspace

KW - Gauss–Laurent quadrature

KW - Matrix function evaluation

KW - Orthogonal Laurent polynomial

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EP - 1964

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 4

ER -

Gauss–Laurent-type quadrature rules for the approximation of functionals of a nonsymmetric matrix

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Keywords

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