Foundations of Computational Mathematics

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

Ronald Devore (Edited by), Arieh Iserles (Edited by), Endre Süli (Edited by)

9780521003490, Cambridge University Press

Paperback, published 17 May 2001

412 pages, 51 b/w illus. 4 tables
22.8 x 15.3 x 2.4 cm, 0.579 kg

'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)

The Society for the Foundations of Computational Mathematics supports fundamental research in a wide spectrum of computational mathematics and its application areas. As part of its endeavour to promote research in computational mathematics, the society regularly organises 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, optimisation, computational geometry, stochastic systems and the computation of partial differential equations. The wide range of topics covered illustrates the diversity of contemporary computational mathematics and the intricate web of its interaction with pure mathematics and application areas. This book will be of interest to researchers and graduate students in all areas of mathematics involving numerical and symbolic computations.

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.

Subject Areas: Mathematical theory of computation [UYA], Numerical analysis [PBKS]