Tensor Spaces and Numerical Tensor Calculus (Springer Series in Computational Mathematics, 56)
Brand: Springer
Categories: Books, Science & Math, Chemistry



Dimensions: 6.14 x 1.38 x 9.21 inches
Language: English
ISBN-10: 3030355535
Publisher: Springer
Print length: 633 pages
Publication date: January 24, 2020
ISBN-13: 978-3030355531
Edition: 2nd ed. 2019
Part of series: Springer Computational Mathematics
subtitle: 2nd ed. 2019 Edition
author: Wolfgang Hackbusch
review: Editorial Reviews From the Back Cover Special numerical techniques are already needed to deal with n × n matrices for large n . Tensor data are of size n × n ×...× n = 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. 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. About the Author 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.