Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus
Gebonden Engels 2012 2012e druk 9783642280269Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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.
Specificaties
ISBN13:9783642280269
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:500
Uitgever:Springer Berlin Heidelberg
Druk:2012
Lezersrecensies
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Inhoudsopgave
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.
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