A global rational Arnoldi method for model reduction

Abidi, O.; Hached, Mustapha; Jbilou, Khalide

doi:10.1016/j.cam.2017.05.003

Cited by 3 publications

(3 citation statements)

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“…Example 1 In this experiment, we consider the nonsymmetric matrices A 1 and A 2 given in [34] and [1], respectively. These matrices were obtained from the centered finite difference discretization (CFDD) of the elliptic operators L 1 (u) and L 2 (u), respectively, L 1 (u) = −∆ u + 50(x + y)u x + 50(x + y)u y .…”

Section: Algorithmmentioning

confidence: 99%

“…The superscript T denotes transposition. The need to evaluate matrix functions of the forms (1) arises in various applications such as in network analysis [16], machine learning [29], electronic structure computation [4,32] and the solution of ill-posed problems [17,21]. When the matrix A is a small to meduim size, the matrix function f (A) can be determined by the spectral factorization of A; see [23,21], for discussions on several possible definitions of matrix functions.…”

Section: Introductionmentioning

confidence: 99%

“…[20,30,12,13,14,28]. In this paper, we present the global extended-rational Arnoldi method to approximate the matrix function (1). The extended-rational Arnoldi method was proposed and applied to model reduction by [2].…”

Section: Introductionmentioning

confidence: 99%

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The global extended-rational Arnoldi method for matrix function approximation

Bentbib,

Ghomari,

Jbilou

2020

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The numerical computation of matrix functions such as f (A)V , where A is an n × n large and sparse square matrix, V is an n × p block with p ≪ n and f is a nonlinear matrix function, arises in various applications such as network analysis ( f (t) = exp(t) or f (t) = t 3 ), machine learning ( f (t) = log(t)), theory of quantum chromodynamics ( f (t) = t 1/2 ), electronic structure computation, and others. In this work, we propose the use of global extended-rational Arnoldi method for computing approximations of such expressions. The derived method projects the initial problem onto an global extended-rational Krylov sub-An adaptive procedure for the selection of shift parameters {s 1 , . . . , s m } is given. The proposed method is also applied to solve parameter dependent systems. Numerical examples are presented to show the performance of the global extended-rational Arnoldi for these problems.

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Section: Algorithmmentioning

confidence: 99%