Tensor Spaces and Numerical Tensor Calculus

Wolfgang Hackbusch

ISBN 10: 3030355535 / ISBN 13: 9783030355531

Edité par Springer International Publishing, 2020

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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 includesnew 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.

N° de réf. du vendeur 9783030355531

Détails bibliographiques

• Titre: Tensor Spaces and Numerical Tensor Calculus
• Éditeur: Springer International Publishing
• Date de parution: 2020
• Langue: anglais
• ISBN à 10 chiffres: 3030355535
• ISBN à 13 chiffres: 9783030355531
• Reliure: Buch
• Édition: 2ème Édition
• État de l'article: Neu

A propos de ce titre

Synopsis

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.

À propos de l?auteur

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.