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Journal of Scientific Computing

Erschienen in:

08.01.2016

Solving Multi-linear Systems with \(\mathcal {M}\)-Tensors

verfasst von: Weiyang Ding, Yimin Wei

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2016

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Abstract

This paper is concerned with solving some structured multi-linear systems, especially focusing on the equations whose coefficient tensors are \(\mathcal {M}\)-tensors, or called \(\mathcal {M}\)-equations for short. We prove that a nonsingular \(\mathcal {M}\)-equation with a positive right-hand side always has a unique positive solution. Several iterative algorithms are proposed for solving multi-linear nonsingular \(\mathcal {M}\)-equations, generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, we apply the \(\mathcal {M}\)-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.

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Titel: Solving Multi-linear Systems with -Tensors
verfasst von: Weiyang Ding
Yimin Wei
Publikationsdatum: 08.01.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0156-7

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