Andreas Frommer - Böcker

The Third International Workshop on Numerical Analysis and Lattice QCD tookplaceattheUniversityofEdinburgh fromJune30th toJuly4th,2003. It continued a sequence which started in 1995 at the University of Kentucky and continuedin1999withaworkshopattheUniversityofWuppertal.Theaimof these workshops is to bring together applied mathematicians and theoretical physicists to stimulate the exchange of ideas between leading experts in the ?elds of lattice QCD and numerical analysis. Indeed, the last ten years have seen quite a substantial increase in cooperation between the two scienti?c communities, and particularly so between numerical linear algebra and lattice QCD. The workshop was organised jointly by the University of Edinburgh and the UK National e-Science Centre. It promoted scienti?c progress in lattice QCD as an e-Science activity that encourages close collaboration between the core sciences of physics, mathematics, and computer science. In order to achieve more realistic computations in lattice quantum ?eld theory substantial progress is required in the exploitation of numerical me- ods.Recently,therehasbeenmuchprogressintheformulationoflatticechiral symmetry satisfying the Ginsparg-Wilson relation.Methods for impleme- ing such chiral fermions e?ciently were the principal subject of this meeting, which, in addition, featured several tutorial talks aiming at introducing the important concepts of one ?eld to colleagues from the other. These proce- ings re?ect this, being organised in three parts: part I contains introductory surveypapers,whereaspartsIIandIIIcontainlatestresearchresultsinlattice QCD and in computational methods.

This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 03041 on Numerical Software with Result Verification held at Dagstuhl Castle, Germany, in January 2003. The 18 revised full papers presented were selected during two rounds of reviewing and improvements. The papers are organized in topical sections on languages, software systems and tools, new verification techniques based on interval arithmetic, applications in science and engineering, and novel approaches to verification.

The book with contributions from the joint interdisciplinary workshop covers important numerical bottleneck problems from lattice quantum chromodynamics: 1) The computation of Green's functions from huge sparse linear systems and the determination of flavor-singlet observables by stochastic estimates of matrix traces can both profit from novel preconditioning techniques and algebraic multi-level algorithms. 2) The exciting overlap fermion formulation requires the solution of linear systems including a matrix sign function, an extremely demanding numerical task that is tackled by Lanczos/projection methods. 3) Realistic simulations of QCD must include three light dynamical quark flavors with non-degenerate masses. Algorithms using polynomial approximations of the matrix determinant can deal with this situation. The volume aims at stimulating synergism and creating new links between lattice quantum and numerical analysis.