The birth of numerical analysis / editors, Adhemar Bultheel, Ronald Cools.

Format:

Book

Contributor:

Bultheel, Adhemar.

Cools, Ronald.

Katholieke Universiteit te Leuven (1970- ). Departement Computerwetenschappen.

Language:

English

Subjects (All):

Numerical analysis--Congresses.

Numerical analysis.

Numerical analysis--History--Congresses.

Physical Description:

1 online resource (240 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, c2010.

Language Note:

English

Summary:

The 1947 paper by John von Neumann and Herman Goldstine, "Numerical Inverting of Matrices of High Order" (<i>Bulletin of the AMS</i>, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. <i>Sample Chapter(s)</i><br>Chapter 1: Some pioneers of extrapolation methods (323 KB)<br

Contents:

Table of Contents; Preface; 1 The limitations of computers; 2 A birthday?; 3 Sixty years young ""back to the roots of the future""; 4 Extrapolation; 5 Functional equations; 6 The importance of software and the influence of hardware; 7 Approximation and optimization; 8 And some history; 9 And there is more; 10 Acknowledgements; Some pioneers of extrapolation methods Claude Brezinski; 1 Interpolation, extrapolation, sequence transformations; 2 Richardson's extrapolation; 2.1 First contributions; 2.2 C. Huygens; 2.3 L.F. Richardson; 2.4 W. Romberg; 3 Aitken's process and Steffensen's method

3.1 Seki Takakazu3.2 A.C. Aitken; 3.3 J.F. Steffensen; 3.4 D. Shanks; 3.5 P. Wynn; 4 And now?; References; Very basic multidimensional extrapolation quadrature James N. Lyness; 1 Introduction; 1.1 Software; 1.2 N-dimensional quadrature rules; 2 Extrapolation quadrature for regular integrands; 2.1 One dimension; regular integrand; 2.2 N-Dimensional square and simplex; regular integrand; 3 Extrapolation quadrature for some N-dimensional algebraic singularities; 3.1 An N-dimensional example; 3.2 Homogeneous type singularities; 4 Choice of mesh sequence

5 Gaussian formulas for singular integrands6 Concluding remarks; References; Numerical methods for ordinary differential equations: early days John C. Butcher; 1 Introduction; 2 Notable events, ideas and people; 3 First contacts with numerical analysis; References; Interview with Herbert Bishop Keller Hinke M. Osinga; Developing a taste for dynamical system theory; Retirement; Addicted to cycling; A personal perspective on the history of the numerical analysis of Fredholm integral equations of the second kind Kendall Atkinson; 1 Introduction; 2 A survey of numerical methods

2.1 Degenerate kernel approximation methods2.2 Projection methods; 2.3 Nystrom methods; 3 Error analysis and some history; 3.1 Degenerate kernel methods; 3.2 Projection methods; 3.2.1 Kantorovich and Krylov regularization; 3.2.2 The iterated projection solution; 3.3 Nystrom methods; 3.3.1 Product integration; 3.3.2 The eigenvalue problem; 3.4 Iterative variants; 4 Boundary integral equation methods; Acknowledgements.; References; Memoires on building a general purpose numerical algorithms library Brian Ford; 1 Introduction; 2 Prelude - the pre-NAG days; 3 Announcement of the ICL 1906A

4 Birth of the NAG Library - built collaboratively5 Selection of library contents; 6 Library contents; 7 Comments on the chapter contents developed; 8 Chapter subdivisions; 9 Library contribution; 10 Three chapter case studies; 10.1 Numerical linear algebra; 10.2 Curve and surface fitting, and interpolation; 10.3 Ordinary differential equations; 11 Types of Library Software; 12 Library construction and operation - the NAG Library Machine; 13 Issues of numerical software portability; 14 NAG Library Conceptual Machine; 15 Models of portability for numerical software; 16 NAG Library Manual

17 Software testing

Notes:

Proceedings of a symposium held at the Department of Computer Science of the K.U. Leuven, October 29-30, 2007.

Includes bibliographical references and indexes.

ISBN:

9786612760594

9781282760592

1282760599

9789812836267

9812836268

OCLC:

630133838