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

Hardcover | April 30, 1999

byArthur G. Werschulz

not yet rated|write a review
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 adifferential 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 analystsworking on the approximate solution of differential and integral equations as well as to complexity theorists addressing related questions in this area.

Pricing and Purchase Info

$243.00

Ships within 1-3 weeks
Ships free on orders over $25

From the Publisher

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 adifferential operator. The function f may n...

Arthur G. Werschulz, Associate Professor of Mathematics and Computer Science, Fordham University; Visiting Scholar, Columbia University.
Format:HardcoverDimensions:340 pages, 9.21 × 6.14 × 0.01 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198535899

ISBN - 13:9780198535898

Customer Reviews of The Computational Complexity of Differential and Integral Equations: An Information-Based Approach

Reviews

Extra Content

Editorial Reviews

'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.