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Tensor Spaces and Numerical Tensor Calculus de Wolfgang Hackbusch

Tensor Spaces and Numerical Tensor Calculus: Springer Series in Computational Mathematics, cartea 42

Autor Wolfgang Hackbusch
en Limba Engleză Paperback – 12 apr 2014
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.
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Specificații

ISBN-13: 9783642427091
ISBN-10: 364242709X
Pagini: 524
Dimensiuni: 155 x 235 x 28 mm
Greutate: 0.73 kg
Ediția:2012
Editura: Springer
Colecția Springer
Seria Springer Series in Computational Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Recenzii

“The present book Tensor spaces and numerical tensorcalculus by Wolfgang Hackbusch to a large extent fills the gap between theoryon finite-dimensional tensor spaces and tensor computations. It also gives acomprehensive overview of numerical tensor computations. … the book is mostuseful as a (very rich) source book for researchers in the area. It might also beused as a textbook for a Ph.D. course … .” (Lars Eldén, Mathematical Reviews,October, 2015)

Textul de pe ultima copertă

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.

Caracteristici

First monograph on this subject in the field of numerical mathematics
Contains algebraic and functional analysis aspects of tensor spaces
Focuses on the numerical treatment ​

Cuprins

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.

Notă biografică

Wolfgang Hackbusch 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.