Bounds For The Greatest Eigenvalue And Greatest Singular Values Of Positive Tensors

Tensor analysis is an important tool in theoretical physics, continuum mechanicsand many other areas of science and engineering. In recent years, the largest eigenvalueproblem for nonnegative tensors has attracted special attention. In this paper, wemainly investigate the bounds for the greatest eigenvalue and maximal eigenvectors ofpositive square tensors, the bounds for the largest singular value of positive rectangulartensors. The full text is divided into four parts.In the first part, we briefly introduce the research background and current situationof the tensor, and probe into the main content of the paper.In the second part, we recall the basic concepts of tensors.In the third part, we introduce the bounds for the greatest eigenvalue and maximaleigenvectors of positive square tensors and report a numerical example.In the fourth part, we mainly investigate the bounds for the largest singular valueof positive rectangular tensors.