Theory and Computation of Complex Tensors and its Applications
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Beschreibung
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.
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
Autor*in
Maolin Che
Themen in »Theory and Computation of Complex Tensors and its Applications«
tensor spectral theory tensor complementarity problems nonnegative tensors U-eigenpairs randomized algorithms US-eigenvalues randomized algorithms matrix theory