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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2022

01-04-2022

Generalized Fractional Algebraic Linear System Solvers

Authors: X. Antoine, E. Lorin

Published in: Journal of Scientific Computing | Issue 1/2022

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Abstract

This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that is finding x solution to \(\sum _{\alpha \in \mathbb {R}}A^{\alpha }x=b\). These systems will be referred to as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive several gradient methods for solving these very computationally complex problems, which themselves require the solution to intermiediate standard Fractional Algebraic Linear Systems (FALS) \(A^{\alpha }x=b\), with \(\alpha \in \mathbb {R_+}\). The latter usually require the solution to many classical linear systems \(Ax=b\). We also show that in some cases, the solution to a GFALS problem can be obtained as the solution to a first-order hyperbolic system of conservation laws. We also discuss the connections between this PDE-approach and gradient-type methods. The convergence analysis is addressed and some numerical experiments are proposed to illustrate and compare the methods which are proposed in this paper.
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Appendix
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Metadata
Title
Generalized Fractional Algebraic Linear System Solvers
Authors
X. Antoine
E. Lorin
Publication date
01-04-2022
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2022
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-022-01785-z

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