Foundations of Computational Mathematics

ISBN-13: 9780521003490 / Angielski / Miękka / 2001 / 412 str.

DeVore Iserles Suli;DeVore/Iserles/Suli; Endre Suili

Opis

The Society for the Foundations of Computational Mathematics supports fundamental research in a wide spectrum of computational mathematics and its application areas. It regularly organizes conferences and workshops which bring together leading researchers in the diverse fields impinging on all aspects of computation. This book presents thirteen papers written by plenary speakers from the 1999 conference, all of whom are the foremost figures in their respective fields. Topics covered include complexity theory, approximation theory, optimization, computational geometry, stochastic systems and the computation of partial differential equations.

Recenzje

'Each chapter provides a readable and comprehensive introduction to and overview of its topic, and in many cases also presents new research results. Collectively the chapters provide a very clear indication of the enormous breadth of computational mathematics, its close interaction with other developments within mathematics, and its impact in both mathematics and applications.' ZAMM (Zeitschrift für Angewandte Mathematik und Mechanik)

Spis treści

Preface; 1. Singularities and computation of minimizers for variational problems J. M. Ball; 2. Adaptive finite element methods for flow problems R. Becker, M. Braack and R. Rannacher; 3. Newton's method and some complexity aspects of the zero-finding problem J.-P. Dedieu; 4. Kronecker's smart little black boxes M. Giusti and J. Heintz; 5. Numerical analysis in Lie groups A. Iserles; 6. Feasibility control in nonlinear optimization M. Marazzi and J. Nocedal; 7. Six lectures on the geometric integration of ODEs R. I. MaLachlan and G. R. Quispel; 8. When are integration and discrepancy tractable? E. Novak and H. Wozniakowski; 9. Moving frames - in geometry, algebra, computer vision, and numerical analysis P. J. Olver; 10. Harmonic map flows and image processing G. Sapiro; 11. Statistics from computations H. Sigurgeirsson and A. M. Stuart; 12. Simulation of stochastic processes and applications D. Talay; 13. Real-time numerical solution to Duncan-Mortensen-Zakai equation S.-T. Yau and S. S.-T. Yau.