Foundations of Computational Mathematics, Hong Kong 2008 [Paperback]

Surveys and summaries of the latest research in numerical analysis, optimization, computer algebra and scientific computing.Leading figures in modern computational mathematics present here the latest research and give surveys of its contemporary topics. This is a valuable resource for all working in numerical analysis, optimization, computer algebra and scientific computing.Leading figures in modern computational mathematics present here the latest research and give surveys of its contemporary topics. This is a valuable resource for all working in numerical analysis, optimization, computer algebra and scientific computing.This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insight into the state of the art in this active and significant field.Preface; Contributors; 1. Smoothed analysis of condition numbers Peter B?rgisser; 2. A world of binomials Alicia Dickenstein; 3. Linear and nonlinear subdivision schemes in geometric modeling Nira Dyn; 4. Energy preserving and energy stable schemes for the shallow water equations Ulrik Fjordholm, Siddhartha Mishra and Eitan Tadmor; 5. Pathwise convergence of numerical schemes for random and stochastic differential equations A. Jentzen, P. E. Kloeden and A. Neuenkirch; 6. Some properties of the global behaviour of conservative low-dimensional systems Carles Sim?; 7. A panoramic view of asymptotics R. Wong; 8. Tractability of multivariate problems H. Wozniakowski.