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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.
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 |
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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 |