This volume comprises a set of research papers that together will provide an up-to-date survey of the current state of the art in numerical analysis. The contributions are based on talks given at a conference in honour of Jim Wilkinson, one of the foremost pioneers in numerical analysis. The contributors were all his colleagues and collaborators and are leading figures in their respective fields.

The breadth of Jim Wilkinson's research is reflected in the main themes covered: linear algebra, error analysis and computer arithmetic, algorithms, and mathematical software. Particular topics covered include analysis of the Lanczos algorithm, determining the nearest defective matrix to a given one, QR-factorizations, error propagation models, parameter estimation problems, sparse systems, and shape-preserving splines.

As a whole the volume reflects the current vitality of numerical analysis and will prove an invaluable reference for all numerical analysts.

Contenuti

List of contributors; Gene Golub: Prologue: Reflections on Jim Wilkinson; Beresford Parlett: Misconvergence in the Lanczos algorithm; Charles L. Lawson & Kajal K. Gupta: The Lanczos algorithm for a pure imaginary Hermitian matrix; James Demmel: Nearest defective matrices and the geometry of ill-conditioning; Theo Beelen & Paul Van Dooren: Computational aspects of the Jordan canonical form; C.C. Paige: Some aspects of generalized QR factorizations; I.S. Duff, N.I.M. Gould, M. Lescrenier, & J.K. Reid: The multifrontal method in a parallel environment; Philip E. Gill, Walter Murray, Michael A. Saunders, & Margaret H. Wright: A Schur-complement method for sparse quadratic programming; Fran�oise Chatelin & Marie Christine Brunet: A probabilistic round-off error propagation model application to the eigenvalue problem; Nicholas J. Higham: Analysis of the Cholesky decomposition of a semi-definite matrix; James M. Varah: On the conditioning of parameter estimation problems; F.W.J. Olver: Rounding errors in algebriac process ― in level-index arithmetic; Mario Arioli & Iain S. Duff: Experiments in tearing large sparse systems; M.G. Cox: The least-squares solution of linear equations with block-angular observation matrix; G.W. Stewart: An iterative method for solving linear inequalities; Ake Bj�rck; Advances in reliable numerical computing; Christian H. Reinsch: Software for shape-preserving spline interpolation; D.A.H. Jacobs & G Markham: Experiences with some software engineering practices in numerical software; Jack Dongarra & Sven Hammarling: Evolution of numerical software for dense linear algebra; L. Fox: Epilogue: Jim Wilkinson; some after-dinner sentiments.

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