Authors:
- First monograph on this subject in the field of numerical mathematics
- Covers algebraic and functional analysis aspects of tensor spaces
- Focuses on the numerical treatment
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 56)
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Table of contents (17 chapters)
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Front Matter
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Algebraic Tensors
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Front Matter
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Functional Analysis of Tensor Spaces
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Front Matter
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Numerical Treatment
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Front Matter
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About this book
Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd 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. This monograph 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 partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.
Authors and Affiliations
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Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Wolfgang Hackbusch
About the author
Bibliographic Information
Book Title: Tensor Spaces and Numerical Tensor Calculus
Authors: Wolfgang Hackbusch
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-030-35554-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-35553-1Published: 24 January 2020
Softcover ISBN: 978-3-030-35556-2Published: 24 January 2021
eBook ISBN: 978-3-030-35554-8Published: 16 December 2019
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 2
Number of Pages: XXVIII, 605
Number of Illustrations: 5 b/w illustrations, 3 illustrations in colour
Topics: Numerical Analysis, Theoretical and Computational Chemistry, Theoretical, Mathematical and Computational Physics