rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Tensor Spaces and Numerical Tensor Calculus
  name:
    name part: Hackbusch, Wolfgang.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXIV, 500 p. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Wolfgang Hackbusch.
  subject:
    topic: Mathematics
  subject:
    topic: Chemistry, Physical and theoretical
  subject:
    topic: Numerical analysis
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Numerical Analysis
  subject:
    topic: Theoretical and Computational Chemistry
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  classification: QA297-299.4
  classification: 518
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Series in Computational Mathematics, 42
  identifier: 9783642280276
  identifier: http://dx.doi.org/10.1007/978-3-642-28027-6
  record info:
    record creation date: 120223
    record change date: 20151029231402.0
    record identifier: 978-3-642-28027-6