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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.
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.
Details
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
Artikel-ID: 119721393

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