Estimations on upper and lower bounds of solutions to a class of tensor complementarity problems

Abstract

We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, B-tensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP; and hence, they are very easy to calculate.

Keywords

School of Mathematics / Tianjin University / Tianjin 300350 / China

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2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature