Foundations of computational mathematics
著者
書誌事項
Foundations of computational mathematics
（London Mathematical Society lecture note series, 284）
Cambridge University Press, 2001
- : pbk
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注記
Includes bibliographies
内容説明・目次
内容説明
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.
目次
- 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.
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