Tensor Spaces and Numerical Tensor Calculus
1st Edition
Published on 23. February 2012
XXIV, 500 pages
978-3-642-28027-6 (ISBN)
Description
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.
Reviews / Votes
"The present book Tensor spaces and numerical tensor calculus by Wolfgang Hackbusch to a large extent fills the gap between theory on finite-dimensional tensor spaces and tensor computations. It also gives a comprehensive overview of numerical tensor computations. . the book is most useful as a (very rich) source book for researchers in the area. It might also be used as a textbook for a Ph.D. course . ." (Lars Eldén, Mathematical Reviews, October, 2015)
More details
Other editions
Additional editions
Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus
Book
04/2014
Springer
€117.69
Article exhausted; check for reprint
Wolfgang Hackbusch
Tensor Spaces and Numerical Tensor Calculus
Book
02/2012
Springer
€171.19
Article exhausted; check for reprint
Person
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.
Content
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.
