Generalized tensor equations with leading structured tensors

Weijie Yan, Chen Ling, Liyun Ling and Hongjin He

Applied Mathematics and Computation, 2019, vol. 361, issue C, 311-324

Abstract: Systems of tensor equations (TEs) have received much considerable attention in the recent literature. In this paper, we consider a class of generalized tensor equations (GTEs). An important difference between GTEs and TEs is that GTEs can be regarded as a system of non-homogenous polynomial equations, whereas TEs is a homogenous one. Such a difference usually make the theoretical and algorithmic results tailored for TEs not necessarily applicable to GTEs. To study properties of the solution set of GTEs, we first introduce a new class of so-named Z+-tensors, which includes the set of all P-tensors as a proper subset. With the help of degree theory, we prove that the system of GTEs with a leading coefficient Z+-tensor has at least one solution for any right-hand side vector. Moreover, we study the local error bounds under some appropriate conditions. Finally, we employ a Levenberg-Marquardt algorithm to find a solution to GTEs and report some preliminary numerical results.

Keywords: Generalized tensor equations; Z+-tensor; P-tensor; Error bound; Levenberg-Marquardt algorithm (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319304448
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:311-324

DOI: 10.1016/j.amc.2019.05.042

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().