Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch (Autor)

Buch | Softcover

XXIV, 500 Seiten

2014 | 2012
Springer Berlin (Verlag)
978-3-642-42709-1 (ISBN)

Titel erscheint in neuer Auflage

Artikel merken

This book describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of pde and more.

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 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.

The author is working in the field of numerical mathematics for partial differential equations and integral equations. He has published monographs, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and about the technique of hierarchical matrices.

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.

Erscheint lt. Verlag	13.4.2014
Reihe/Serie	Springer Series in Computational Mathematics ; 42
Zusatzinfo	XXIV, 500 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	784 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Chemie ► Physikalische Chemie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	high-dimensional problems • numerical tensor calculus • tensor formats • tensorization • Tensor Spaces
ISBN-10	3-642-42709-X / 364242709X
ISBN-13	978-3-642-42709-1 / 9783642427091
Zustand	Neuware