Some Studies On Tensor Completion And Tensor Eigenvalues

A tensor is an array of high-dimensional data and can be regarded as a high-order generalization of a matrix.Tensors have important applications in some fields,such as psychometrics,signal processing,neuroscience,numerical linear algebra,data mining,graph analysis and so on.Recently,the study of tensor theories focuses on tensor decompositions and tensor eigenvalues.This paper mainly introduces a feasible model for tensor completion and some results on the spectral radii of nonnegative tensors.This paper falls into four parts.In the first part,we briefly introduce the development of tensor decompositions and tensor eigenvalues.In the second part,we mainly introduce optimization models for tensor completion,including a general model which has been accepted by many researchers and a new feasible model based on balanced unfoldings of tensors.In the third part,the Birkhoff-Hopf Theorem of H-spectral radius for positive tensors is given and upper bounds of Z-spectral radius for nonnegative tensors are also presented.In the last part,we carry on a summary of tensor completion and eigenvalues of nonnegative tensors and point out the further research work.