Tensor Spaces and Numerical Tensor Calculus (eBook)

Wolfgang Hackbusch (Autor)

eBook Download: PDF

2012 | 2012
XXIV, 500 Seiten
Springer Berlin (Verlag)
978-3-642-28027-6 (ISBN)

Infos

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.

Inhalt

Tensor Spaces and Numerical Tensor Calculus 4
Preface 8
Contents 10
List of Symbols and Abbreviations 20
Part I Algebraic Tensors 26
Part II Functional Analysis of Tensor Spaces 110
Part III Numerical Treatment 222
References 512
Index 520

Produkt-Details

• Erscheint lt. Verlag: 23.2.2012
• Reihe/Serie: Springer Series in Computational Mathematics
• Reihe/Serie: Springer Series in Computational Mathematics
• Zusatzinfo: XXIV, 500 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: high-dimensional problems • numerical tensor calculus • tensor formats • tensorization • Tensor Spaces
• ISBN-10: 3-642-28027-7 / 3642280277
• ISBN-13: 978-3-642-28027-6 / 9783642280276