Tensor Spaces and Numerical Tensor Calculus

• Κύριος συγγραφέας: Hackbusch, Wolfgang (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Σειρά: Springer Series in Computational Mathematics, 42
• Θέματα: 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...

Πίνακας περιεχομένων:

• 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.