Tensor Spaces and Numerical Tensor Calculus

• Main Author: Hackbusch, Wolfgang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: Springer Series in Computational Mathematics, 42
• Subjects: Mathematics.; Chemistry, Physical and theoretical.; Numerical analysis.; Physics.; Numerical Analysis.; Theoretical and Computational Chemistry.; Theoretical, Mathematical and Computational Physics.

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 trea...

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.