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 Takakazu -- 3.2 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 integrands -- 6 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 methods -- 2.2 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 collaboratively -- 5 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 -- 18 Algorithm testing -- 19 Validation and library assembly -- 20 Software certification -- 21 Implementation and distribution to sites -- 22 Operational principles -- 23 Conclusions -- References -- Recent trends in high performance computing Jack J. Dongarra, Hans W. Meuer, Horst D. Simon, and Erich Strohmaier -- 1 Introduction -- 2 A short history of supercomputers -- 3 2000-2005: Cluster, Intel processors, and the Earth Simulator -- 3.1 Explosion of cluster based system -- 3.2 Intel-ization of the processor landscape -- 3.3 The Earth Simulator shock.

3.4 New architectures on the horizon -- 4 2005 and beyond -- 4.1 Dynamic of the market -- 4.2 Consumer and producer -- 4.3 Performance growth -- 4.4 Projections -- References -- Nonnegativity constraints in numerical analysis Donghui Chen and Robert J. Plemmons -- 1 Historical comments on enforcing nonnegativity -- 2 Preliminaries -- 3 Nonnegative least squares -- 3.1 Introduction -- 3.2 Numerical approaches and algorithms -- 3.2.1 Active-set methods -- 3.2.2 Algorithms based on iterative methods -- 3.2.3 Other methods: -- 4 Nonnegative matrix and tensor factorizations -- 4.1 Nonnegative matrix factorization -- 4.2 Nonnegative tensor decomposition -- 5 Some applications of nonnegativity constraints -- 5.1 Support vector machines -- 5.2 Image processing and computer vision -- 5.3 Text mining -- 5.4 Environmetrics and chemome -- 5.5 Speech recognition -- 5.6 Spectral unmixing by NMF and NTF -- 6 Summary -- References -- On nonlinear optimization since 1959 M. J. D. Powell -- 1 Earlier algorithms -- 2 Two major advances in unconstrained optimization -- 3 Unconstrained objective functions for constrained problems -- 4 Sequential quadratic programming -- 5 Trust region methods -- 6 Further remarks -- Acknowledgement -- References -- The history and development of numerical analysis in Scotland: a personal perspective G. Alistair Watson -- 1 Introduction -- 2 Edinburgh: early years -- 3 How I became a numerical analyst -- 4 St Andrews -- 5 Collaboration between St Andrews and Edinburgh -- 6 Dundee -- 7 The evolution of computing facilities in Dundee -- 8 Postscript -- References -- Remembering Philip Rabinowitz Philip J. Davis and Aviezri S. Fraenkel -- Philip J. Davis -- Aviezri S. Fraenkel 4 -- My early experiences with scientific computation Philip J. Davis.

Applications of Chebyshev polynomials: from theoretical kinematics to practical computations Robert Piessens -- 1 Introduction -- 2 Properties of the Chebyshev polynomials -- 3 Inversion of the Laplace transform -- 4 Solution of the Abel integral equation -- 5 The computation of Laplace, Fourier and Hankel transforms -- 6 Solution of integral equations of the second kind using modified moments -- 7 An extension of Clenshaw-Curtis quadrature to oscillating and singular integrals -- 8 Chebyshev polynomials in QUADPACK -- 9 Conclusion -- References -- Name Index -- Subject Index.