Numerical challenges in lattice quantum chromodynamics

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Lattice gauge theory, a relatively new field in Theoretical Particle Physics, holds significant promise for an ab-initio approach to the nonperturbative aspects of strong interactions. Since its early days, the simulation of quantum chromodynamics (QCD) has drawn interest from numerical analysts, fostering interdisciplinary collaboration between theoretical physicists and applied mathematicians to tackle the challenges of this approach. This volume features contributions from the workshop "Numerical Challenges in Lattice Quantum Chromodynamics," organized by the Institute of Applied Computer Science at Wuppertal University and the Von-Neumann-Institute-for-Computing in August 1999. The workshop aimed to facilitate the exchange of ideas between the lattice QCD and numerical analysis communities, with leading experts emphasizing the need to bridge the gap between these disciplines. Key discussions centered on numerical bottlenecks, such as the computation of Green's functions and the inverse of the Dirac operator. This involves solving large sparse linear systems, particularly in the limit of small quark masses, which leads to high condition numbers of the Dirac matrix. Additionally, the determination of flavor-singlet observables has gained prominence in recent years, further highlighting the complexities faced in this research area.