Overview
- 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
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About this book
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.
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.
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Table of contents (8 chapters)
Authors and Affiliations
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Bibliographic Information
Book Title: Theory and Computation of Complex Tensors and its Applications
Authors: Maolin Che, Yimin Wei
DOI: https://doi.org/10.1007/978-981-15-2059-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2020
Hardcover ISBN: 978-981-15-2058-7Published: 02 April 2020
Softcover ISBN: 978-981-15-2061-7Published: 02 April 2021
eBook ISBN: 978-981-15-2059-4Published: 01 April 2020
Edition Number: 1
Number of Pages: XII, 250
Number of Illustrations: 26 b/w illustrations, 22 illustrations in colour
Topics: Linear and Multilinear Algebras, Matrix Theory, Numerical Analysis, Differential Geometry