Numerical Challenges in Lattice Quantum Chromodynamics : Joint Interdisciplinary Workshop of John von Neumann Institute for Computing Jülich and Institute of Applied Computer Science Wuppertal University August 1999 The book with contributions from the joint interdisciplinary workshop covers important numerical bottleneck problems from lattice quantum chromodynamics: 1) The computation of Greens 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