Newton’s Method for M-Tensor Equations

Dong-Hui Li (), Jie-Feng Xu () and Hong-Bo Guan ()
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Dong-Hui Li: South China Normal University
Jie-Feng Xu: South China Normal University
Hong-Bo Guan: South China Normal University

Journal of Optimization Theory and Applications, 2021, vol. 190, issue 2, No 12, 628-649

Abstract: Abstract We are concerned with the tensor equations whose coefficient tensors are M-tensors. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend the method to solve the equation with a nonnegative constant term and establish its convergence. At last, we do numerical experiments to test the proposed methods. The results show that the proposed methods are quite efficient.

Keywords: M-tensor equation; Newton method; Quadratic convergence; 65H10; 65K10; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01904-0

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