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El. knyga: Foundations of Computational Mathematics, Budapest 2011

Edited by (City University of Hong Kong), Edited by (North Carolina State University), Edited by (Technion - Israel Institute of Technology, Haifa), Edited by (Universidad de Buenos Aires, Argentina)
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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.

This volume brings together articles based on the plenary talks at the Foundations of Computational Mathematics 2011 meeting in Budapest. The articles, which reflect the breadth of research within computational mathematics, will appeal to researchers in related areas and non-experts who wish to gain insight into this significant field.

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A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.
Preface vii
Contributors ix
1 The State of the Art in Smale's 7th Problem
1
C. Beltran
2 The Shape of Data
16(29)
G. Carlsson
3 Upwinding in Finite Element Systems of Differential Forms
45(27)
S. H. Christiansen
4 On the Complexity of Computing Quadrature Formulas for SDEs
72(21)
S. Dereich
T. Muller-Gronbach
K. Ritter
5 The Quantum Walk of F. Riesz
93(20)
F. A. Grunbaum
L. Velazquez
6 Modulated Fourier Expansions for Continuous and Discrete Oscillatory Systems
113(16)
E. Hairer
Ch. Lubich
7 The Dual Role of Convection in 3D Navier-Stokes Equations
129(36)
T. Y. Hou
Z. Shi
S. Wang
8 Algebraic and Differential Invariants
165(23)
E. Hubert
9 Through the Kaleidoscope: Symmetries, Groups and Chebyshev-Approximations from a Computational Point of View
188(42)
H. Munthe-Kaas
M. Nome
B. N. Ryland
10 Sage: Creating a Viable Free Open Source Alternative to Magma, Maple, Mathematica, and MATLAB
230
W. Stein
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.