Foundation of Computational Mathematics

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 prescripts 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.

Contents

• Preface
• Singularities and computation of minimizers for variational problems
• Adaptive finite element methods for flow problems
• Newton's method and some complexity aspects of the zero-finding problem
• Kronecker's smart, little black boxes
• Numerical analysis in Lie groups
• Feasibility control in nonlinear optimization
• Six lectures on the geometric integration of ODEs
• When are integration and discrepancy tractable?
• Moving frames - in geometry, algebra, computer vision, and numerical analysis
• Harmonic map flows and image processing
• Statistics from computations
• Simulation of stochastic processes and applications
• Real-time numerical solution to Duncan-Mortensen-Zakai equation