The Foundations of Computational Mathematics meetings are a platform for cross-fertilisation between numerical analysis, mathematics and computer science. This volume is a collection of articles based on plenary presentations, given at the 2011 meeting, by some of the world's foremost authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness 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.
Felipe Cucker is Chair Professor of the Department of Mathematics at the City University of Hong Kong. Teresa Krick is Professor of Mathematics at the University of Buenos Aires. Allan Pinkus is Professor of Mathematics at the Technion - Israel Institute of Technology. Agnes Szanto is Associate Professor of Mathematics at North Carolina State University.
Preface; List of contributors; 1. The state of the art in Smale's 7th problem C. Beltran; 2. The shape of data Gunnar Carlsson; 3. Upwinding in finite element systems of differential forms S. H. Christiansen; 4. On the complexity of computing quadrature formulas for SDEs S. Dereich, T. Muller-Gronbach and K. Ritter; 5. The quantum walk of F. Riesz F. A. Grunbaum and L. Velazquez; 6. Modulated Fourier expansions for continuous and discrete oscillatory systems E. Hairer and Ch. Lubich; 7. The dual role of convection in 3D Navier-Stokes equations T. Y. Hou, Z. Shi and S. Wang; 8. Algebraic and differential invariants Evelyne Hubert; 9. Through the kaleidoscope: symmetries, groups and Chebyshev-approximations from a computational point of view H. Munthe-Kaas, M. Nome and B. N. Ryland; 10. Sage: creating a viable free open source alternative to Magma, Maple, Mathematica and MATLAB W. Stein.