Tensor Spaces and Numerical Tensor Calculus
Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd 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...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2019, 2019
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| Edition: | 2nd ed. 2019 |
| Series: | Springer Series in Computational Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Part I: Algebraic Tensors
- 1 Introduction
- 2 Matrix Tools
- 3 Algebraic Foundations of Tensor Spaces
- Part II: Functional Analysis of Tensor Spaces
- 4 Banach Tensor Spaces
- 5 General Techniques
- 6 Minimal Subspaces
- Part III: Numerical Treatment
- 7 r-Term Representation
- 8 Tensor Subspace Represenation
- 9 r-Term Approximation
- 10 Tensor Subspace Approximation
- 11 Hierarchical Tensor Representation
- 12 Matrix Product Systems
- 13 Tensor Operations
- 14 Tensorisation
- 15 Multivariate Cross Approximation
- 16 Applications to Elliptic Partial Differential Equations
- 17 Miscellaneous Topics