Theory and Computation of Complex Tensors ...

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Sprache: Englisch

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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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 250 S. 26 s/w Illustr. 22 farbige Illustr. 250 p. 48 illus. 22 illus. in color.
ISBN-13:	9789811520617
ISBN-10:	9811520615
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Wei, Yimin Che, Maolin
Auflage:	1st edition 2020
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 15 mm
Von/Mit:	Yimin Wei (u. a.)
Erscheinungsdatum:	02.04.2021
Gewicht:	0,406 kg