Theory and Computation of Complex Tensors and its Applications

The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors.
This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.

Introduces the neural network models and Takagi factorization for the computation of tensor rank-one approximations and US- (U-) eigenvalues Enriches the properties of nonnegative tensors, defines the sign nonsingular tensors and derives a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors Gives adaptive randomized algorithms for the computation of the low multilinear rank approximations and the tensor train approximations of the tensors

Inhalt
Preface.- Introduction.- The pseudo-spectrum theory.- Perturbation theory.- Tensor complementarity problems.- Plane stochastic tensors.- Neural Networks.- US- and U-eigenpairs of complex tensors.- Randomized algorithms.- Bibliography.- Index.