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 reports on progress in numerical methods for Lattice QCD with chiral fermions. It contains a set of pedagogical introductory articles written by experts from both the Applied Mathematics and Lattice Field Theory communities, together with detailed accounts of leading-edge algorithms for the simulation of overlap chiral fermions. Topics covered include: QCD simulations in the chiral regime; Evaluation and approximation of matrix functions; Krylov subspace methods for the iterative solution of linear systems; Eigenvalue solvers. These are complemented by a set of articles on closely related numerical and technical problems in Lattice field Theory."

Surveys.- An Introduction to Lattice Chiral Fermions.- Computing f(A)b for Matrix Functions f.- Computational Methods for the Fermion Determinant and the Link Between Overlap and Domain Wall Fermions.- Monte Carlo Simulations of Lattice QCD.- Lattice QCD.- Determinant and Order Statistics.- Monte Carlo Overrelaxation for SU(N) Gauge Theories.- Improved Staggered Fermions.- Perturbative Landau Gauge Mean Link Tadpole Improvement Factors.- Reversibility and Instabilities in Hybrid Monte Carlo Simulations.- A Finite Baryon Density Algorithm.- The Nucleon Mass in Chiral Effective Field Theory.- Computational Methods.- A Modular Iterative Solver Package in a Categorical Language.- Iterative Linear System Solvers with Approximate Matrix-vector Products.- What Can Lattice QCD Theorists Learn from NMR Spectroscopists?.- Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov SubspaceMethods.- Fast Evaluation of Zolotarev Coefficients.- The Overlap Dirac Operator as a Continued Fraction.