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Tensor Spaces and Numerical Tensor Calculus
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2012.
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| Edición: | 1st ed. 2012. |
| Colección: | Springer Series in Computational Mathematics,
42 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 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.