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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.
The Society for the Foundations of Computational Mathematics supports and promotes fundamental research in computational mathematics and its applications, interpreted in the broadest sense. It fosters interaction among mathematics, computer science and other areas of computational science through its conferences, workshops and publications. As part of this endeavour to promote research across a wide spectrum of subjects concerned with computation, the Society brings together leading researchers working in diverse fields. Major conferences of the Society have been held in Park City (1995), Rio de Janeiro (1997), Oxford (1999), Minneapolis (2002), Santander (2005), Hong Kong (2008), and Budapest (2011). The next conference is expected to be held in 2014. More information about FoCM is available at its website http://focmsociety. org.
The conference in Budapest on July 4 – 14, 2011, was attended by some 450 scientists. FoCM conferences follow a set pattern: mornings are devoted to plenary talks, while in the afternoon the conference divides into a number of workshops, each devoted to a different theme within the broad theme of foundations of computational mathematics. This structure allows for a very high standard of presentation, while affording endless opportunities for cross-fertilization and communication across subject boundaries. Workshops at the Budapest conference were held in the following nineteen fields:
– Approximation theory
– Asymptotic analysis and high oscillation
– Computational algebraic geometry
– Computational dynamics
– Computational harmonic analysis, image and signal processing
– Computational number theory
– Continuous optimization
– Flocking, swarming, and control of distributed systems
– Foundations of numerical PDEs
– Geometric integration and computational mechanics
– Information-based complexity
– Learning theory
– Multiresolution and adaptivity in numerical PDEs
– Numerical linear algebra
– Random matrix theory, computations & applications