Author	Hackbusch, Wolfgang. author
Title	Tensor Spaces and Numerical Tensor Calculus [electronic resource] / by Wolfgang Hackbusch
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2012
Connect to	http://dx.doi.org/10.1007/978-3-642-28027-6
Descript	XXIV, 500p. 9 illus., 3 illus. in color. online resource

Special numerical techniques are already needed to deal with nxn matrices for large n. Tensor data are of size nxnx...xn=n̂d, where n̂d 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

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

1. Mathematics
2. Chemistry
3. Numerical analysis
4. Mathematics
5. Numerical Analysis
6. Theoretical and Computational Chemistry
7. Theoretical
8. Mathematical and Computational Physics