Custom cover image
Custom cover image

Tensor Spaces and Numerical Tensor Calculus / by Wolfgang Hackbusch

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Series in Computational Mathematics ; 42 | SpringerLink Bücher | Springer eBook Collection Mathematics and StatisticsPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: Online-Ressource (XXIV, 500p. 9 illus., 3 illus. in color, digital)ISBN:
  • 9783642280276
Subject(s): Additional physical formats: 9783642280269 | Buchausg. u.d.T.: Tensor spaces and numerical tensor calculus. Berlin : Springer, 2012. XXIV, 500 S.MSC: MSC: *65F30 | 65-02 | 15A72 | 15A69 | 53A45RVK: RVK: SI 990LOC classification:
  • QA297-299.4
DOI: DOI: 10.1007/978-3-642-28027-6Online resources: Summary: 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.Summary: 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.PPN: PPN: 1651332924Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
No physical items for this record
KIT – The University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT