Theory and Computation of Complex Tensors and its Applications

1. Auflage 2020
ISBN: 978-981-15-2061-7
Verlag: Springer Nature Singapore

Buch, Englisch, 250 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Wei, Yimin

Che, Maolin

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

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.