---

＜電子ブック＞
Tensor Spaces and Numerical Tensor Calculus / by Wolfgang Hackbusch
(Springer Series in Computational Mathematics. ISSN:21983712 ; 56)

版	2nd ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	XXVIII, 605 p. 8 illus., 3 illus. in color : online resource
著者標目	*Hackbusch, Wolfgang author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Chemistry, Physical and theoretical LCSH:Mathematical physics FREE:Numerical Analysis FREE:Theoretical Chemistry FREE:Theoretical, Mathematical and Computational Physics
一般注記	Part I: Algebraic Tensors -- 1 Introduction -- 2 Matrix Tools -- 3 Algebraic Foundations of Tensor Spaces -- Part II: Functional Analysis of Tensor Spaces -- 4 Banach Tensor Spaces -- 5 General Techniques -- 6 Minimal Subspaces -- Part III: Numerical Treatment -- 7 r-Term Representation -- 8 Tensor Subspace Represenation -- 9 r-Term Approximation -- 10 Tensor Subspace Approximation -- 11 Hierarchical Tensor Representation -- 12 Matrix Product Systems -- 13 Tensor Operations -- 14 Tensorisation -- 15 Multivariate Cross Approximation -- 16 Applications to Elliptic Partial Differential Equations -- 17 Miscellaneous Topics Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra HTTP:URL=https://doi.org/10.1007/978-3-030-35554-8

 類似資料