Frontiers of Mathematics in China >
On computing minimal H-eigenvalue of sign-structured tensors
Received date: 06 Feb 2017
Accepted date: 15 Aug 2017
Published date: 27 Nov 2017
Copyright
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.
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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