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Tensor Spaces and Numerical Tensor Calculus

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Tensor Spaces and Numerical Tensor Calculus/ by Wolfgang Hackbusch.
作者:	Hackbusch, Wolfgang.
面頁冊數:	XXVIII, 605 p. 8 illus., 3 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Numerical analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-35554-8
ISBN:	9783030355548

Tensor Spaces and Numerical Tensor Calculus
Hackbusch, Wolfgang.

Tensor Spaces and Numerical Tensor Calculus[electronic resource] /by Wolfgang Hackbusch. - 2nd ed. 2019. - XXVIII, 605 p. 8 illus., 3 illus. in color.online resource. - Springer Series in Computational Mathematics,560179-3632 ;. - Springer Series in Computational Mathematics,48.

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.

ISBN: 9783030355548

Standard No.: 10.1007/978-3-030-35554-8doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

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