The Computational Complexity of Differential and Integral Equations: An Information-Based Approach - Couverture rigide

Werschulz, Arthur G.

 
9780198535898: The Computational Complexity of Differential and Integral Equations: An Information-Based Approach
Couverture rigide
ISBN 10 : 0198535899 ISBN 13 : 9780198535898
Editeur : Oxford University Press, 1991

Synopsis

This book is concerned with a central question in numerical analysis: the approximate solution of differential or integral equations by algorithms using incomplete information. This situation often arises for equations of the form Lu = f, where f is some function defined on a domain and L is a differential operator. The function f may not be given exactly - we might only know its value at a finite number of points in the domain. Consequently the best that can be hoped for is to solve the equation to within a given accuracy at minimal cost or complexity.

The author develops the theory of the complexity of the solutions to differential and integral equations and discusses the relationship between the worst-case setting and other (sometimes more tractable) related settings such as the average case, probabilistic, asymptotic, and randomized settings. Furthermore, he studies to what extent standard algorithms (such as finite element methods for elliptic problems) are optimal.

This approach is discussed in depth in the context of two-point boundary value problems, linear elliptic partial differential equations, integral equations, ordinary differential equations, and ill-posed problems. As a result, this volume should appeal to mathematicians and numerical analysts working on the approximate solution of differential and integral equations as well as to complexity theorists addressing related questions in this area.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book is concerned with a central question in numerical analysis: the approximate solution of differential or integral equations by algorithms using incomplete information. This situation often arises for equations of the form Lu = f, where f is some function defined on a domain and L is a differential operator. The function f may not be given exactly - we might only know its value at a finite number of points in the domain. Consequently the best that can be hoped for is to solve the equation to within a given accuracy at minimal cost or complexity. The author develops the theory of the complexity of the solutions to differential and integral equations and discusses the relationship between the worst-case setting and other (sometimes more tractable) related settings such as the average case, probabilistic, asymptotic, and randomized settings. Furthermore, he studies to what extent standard algorithms (such as finite element methods for elliptic problems) are optimal. This approach is discussed in depth in the context of two-point boundary value problems, linear elliptic partial differential equations, integral equations, ordinary differential equations, and ill-posed problems. As a result, this volume should appeal to mathematicians and numerical analysts working on the approximate solution of differential and integral equations as well as to complexity theorists addressing related questions in this area.

Revue de presse

'This book ... is a most welcome addition to the theoretical computer science and numerical analysis literature. Though it is intended as a summary of current research, it is of the quality that would make it an excellent textbook on the subject for advanced numerical analysis and computer science courses .. it reads easily and lucidly.' R.S. Andersen

'An excellent and accessible introduction to the complexity of basic arithmetic operations ... it adds an interesting new dimension to the study of numerical methods for the solution of PDEs.' Notices of the A.M.S.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Oxford University Press
Date d'édition
1991
Langue
anglais
ISBN 10 
0198535899
ISBN 13 
9780198535898
Reliure
Relié
Nombre de pages
342
Coordonnées du fabricant
non disponible
Personne responsable
Ufficio Anagrafiche Messaggerie
ufficio.anagrafiche@meli.it

Via Verdi, 8
Assago Milano
20090
Italie