QCD and Numerical Analysis III, 2005 Proceedings of the Third International Workshop on Numerical Analysis and Lattice QCD, Edinburgh, June-July 2003 Lecture Notes in Computational Science and Engineering Series, Vol. 47

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.