Study On Spectral Radius Estimation Of Nonnegative Matrices And M Eigenvalues Of Elasticity Tensors

Nonnegative matrices theory is used widely in numerical analysis, graph, computerscience and management science as a fundamental tool. Estimating spectral radius ofnonnegative matrices is one of the main problems in this field. If the bounds of thespectral radius can be expressed as a function of the entries which is easy to compute,then the estimates are more useful. A tensor is a higher order generalization of amatrix, because of the limitation of traditional matrices theory in processing data,tensor analysis becomes a very important tool in science and engineering fields. It playsan important role in many fields such as the signal processing, data communication,computer vision, and image processing. The M eigenvalues of elasticity tensors is oneof the hot spots in the recent research. In this paper we mainly investigate elasticitytensors. The full text is divided into five parts.In the first part we briefly introduce the research background and current situationof nonnegative matrices and elasticity tensors, and point out the main content of thepaper.In the second part we introduce the basic concepts of nonnegative matrices andtensors.In the third part we introduce general methods to local the eigenvalues of matrices,and we obtain two new bounds of spectral radius of nonnegative matrices. Comparedwith the relevant conclusions, the new bounds are more accurate.In the fourth part we mainly consider the M eigenvalues of elasticity tensors.Computational methods for finding M eigenvalues are presented.