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1 online resource (240 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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Intro -- 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 |
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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 |
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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 |
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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 |
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Key Features:This is the first collection of such contributions that appears in book formAll authors are authorities in their subfields who have experienced the evolution and have watched numerical analysis grow to maturity |
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Description based on publisher supplied metadata and other sources |
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries |
| Link |
Print version: Bultheel, Adhemar Birth Of Numerical Analysis, The
Singapore : World Scientific Publishing Company,c2009 9789812836250
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| Subject |
Numerical analysis -- Congresses.;Numerical analysis -- History -- Congresses
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Electronic books
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| Alt Author |
Cools, Ronald
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