Decomposability of Tensors

Buch | Softcover

160 Seiten

2019
MDPI (Verlag)
978-3-03897-590-8 (ISBN)

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Tensor decomposition is a relevant topic, both for theoretical and applied mathematics, due to its interdisciplinary nature, which ranges from multilinear algebra and algebraic geometry to numerical analysis, algebraic statistics, quantum physics, signal processing, artificial intelligence, etc. The starting point behind the study of a decomposition relies on the idea that knowledge of elementary components of a tensor is fundamental to implement procedures that are able to understand and efficiently handle the information that a tensor encodes. Recent advances were obtained with a systematic application of geometric methods: secant varieties, symmetries of special decompositions, and an analysis of the geometry of finite sets. Thanks to new applications of theoretic results, criteria for understanding when a given decomposition is minimal or unique have been introduced or significantly improved. New types of decompositions, whose elementary blocks can be chosen in a range of different possible models (e.g., Chow decompositions or mixed decompositions), are now systematically studied and produce deeper insights into this topic. The aim of this Special Issue is to collect papers that illustrate some directions in which recent researches move, as well as to provide a wide overview of several new approaches to the problem of tensor decomposition."

Dipartimento di Scienze Matematiche e Informatiche, Università degli Studi di Siena, Pian dei Mantellini, 44, 53100 Siena, Italy

Erscheinungsdatum	05.03.2022
Mitarbeit	Gast Herausgeber: Luca Chiantini
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Datenbanken
Themenwelt	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Complexity • Rank, border rank and typical rank • Tensor Analysis
ISBN-10	3-03897-590-7 / 3038975907
ISBN-13	978-3-03897-590-8 / 9783038975908
Zustand	Neuware