RESEARCH ARTICLE

On computing minimal H-eigenvalue of sign-structured tensors

  • Haibin CHEN ,
  • Yiju WANG
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  • School of Management Science, Qufu Normal University, Rizhao 276826, China

Received date: 06 Feb 2017

Accepted date: 15 Aug 2017

Published date: 27 Nov 2017

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany

Abstract

Finding the minimal H-eigenvalue of tensors is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a sum-of-squares (SOS) algorithm for computing the minimal H-eigenvalues of tensors with some sign structures called extended essentially nonnegative tensors (EEN-tensors), which includes nonnegative tensors as a subclass. In the even-order symmetric case, we first discuss the positive semi-definiteness of EEN-tensors, and show that a positive semi-definite EEN-tensor is a nonnegative tensor or an M-tensor or the sum of a nonnegative tensor and an M-tensor, then we establish a checkable sufficient condition for the SOS decomposition of EEN-tensors. Finally, we present an efficient algorithm to compute the minimal H-eigenvalues of even-order symmetric EEN-tensors based on the SOS decomposition. Numerical experiments are given to show the efficiency of the proposed algorithm.

Cite this article

Haibin CHEN , Yiju WANG . On computing minimal H-eigenvalue of sign-structured tensors[J]. Frontiers of Mathematics in China, 2017 , 12(6) : 1289 -1302 . DOI: 10.1007/s11464-017-0645-0

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