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＜E-Book＞
Tensor Spaces and Numerical Tensor Calculus / by Wolfgang Hackbusch
(Springer Series in Computational Mathematics. ISSN:21983712 ; 42)

Edition	1st ed. 2012.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2012
Language	English
Size	XXIV, 500 p : online resource
Authors	*Hackbusch, Wolfgang author SpringerLink (Online service)
Subjects	LCSH:Numerical analysis LCSH:Chemistry, Physical and theoretical LCSH:Mathematical physics FREE:Numerical Analysis FREE:Theoretical Chemistry FREE:Theoretical, Mathematical and Computational Physics
Notes	Part I: Algebraic Tensors -- Introduction -- Matrix Tools -- Algebraic Foundations of Tensor Spaces -- Part II: Functional Analysis of Tensor Spaces -- Banach Tensor Spaces -- General Techniques -- Minimal Subspaces.-Part III: Numerical Treatment -- r-Term Representation -- Tensor Subspace Represenation -- r-Term Approximation -- Tensor Subspace Approximation.-Hierarchical Tensor Representation -- Matrix Product Systems -- Tensor Operations -- Tensorisation -- Generalised Cross Approximation -- Applications to Elliptic Partial Differential Equations -- Miscellaneous Topics -- References -- Index Special numerical techniques are already needed to deal with nxn matrices for large n. Tensor data are of size nxnx...xn=n^d, where n^d 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. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc HTTP:URL=https://doi.org/10.1007/978-3-642-28027-6

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