Numerical Analysis: Historical Developments in the 20th Century

Author： Brezinski   C.;Wuytack   L.  

Publisher： Elsevier Science‎

Publication year： 2012

E-ISBN: 9780444598585

P-ISBN(Paperback): 9780444506177

P-ISBN(Hardback):  9780444506177

Subject： O241 数值分析

Language： ENG

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Description

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

Chapter

Front Cover

pp.：  1 – 4

Numerical Analysis: Historical Developments in the 20th Century

pp.：  4 – 5

Copyright Page

pp.：  5 – 6

Contents

pp.：  6 – 8

Chapter 1. Numerical analysis in the twentieth century

pp.：  8 – 48

Chapter 2. Approximation in normed linear spaces

pp.：  48 – 84

Chapter 3. A tutorial history of least squares with applications to astronomy and geodesy

pp.：  84 – 120

Chapter 4. Convergence acceleration during the 20th century

pp.：  120 – 142

Chapter 5. On the history of multivariate polynomial interpolation

pp.：  142 – 156

Chapter 6. Numerical linear algebra algorithms and software

pp.：  156 – 182

Chapter 7. Iterative solution of linear systems in the 20th century

pp.：  182 – 216

Chapter 8. Eigenvalue computation in the 20th century

pp.：  216 – 248

Chapter 9. Historical developments in convergence analysis for Newton's and Newton-like methods

pp.：  248 – 272

Chapter 10. A survey of truncated-Newton methods

pp.：  272 – 288

Chapter 11. Cubature formulae and orthogonal polynomials

pp.：  288 – 320

Chapter 12. Computation of Gauss-type quadrature formulas

pp.：  320 – 338

Chapter 13. A review of algebraic multigrid

pp.：  338 – 368

Chapter 14. From finite differences to finite elements A short history of numerical analysis of partial differential equations

pp.：  368 – 422

Chapter 15. A perspective on the numerical treatment of Volterra equations

pp.：  422 – 456

Chapter 16. Numerical methods for ordinary differential equations in the 20th century

pp.：  456 – 486

Chapter 17. Retarded differential equations

pp.：  486 – 513

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