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Seit es elektronische Rechenanlagen gibt, verbindet man mit einem nume rischen Verfahren ganz selbstverstandlich auch einen zugehorigen Algorith mus, welcher auf einem Computer iiber ein Programm realisiert werden kann. Um so erstaunlicher scheint es, dafi von seiten der Numerik der algorithmi sche Aspekt lange stark vemachlassigt wurde. In den letzten fiinfzehn J ahren hat sich hier jedoch ein tiefgreifender Wan del vollzogen. Er wurde ausgelost durch den erfolgreichen, inzwischen iiberall verbreiteten Einsatz von Vektorrechnem, welche heute Rechenleistungen bie ten, die bis vor kurzem noch...

Lattice gauge theory is a fairly young research area in Theoretical Particle Physics. It is of great promise as it offers the framework for an ab-initio treatment of the nonperturbative features of strong interactions. Ever since its adolescence the simulation of quantum chromodynamics has attracted the interest of numerical analysts and there is growing interdisciplinary engage ment between theoretical physicists and applied mathematicians to meet the grand challenges of this approach. This volume contains contributions of the interdisciplinary workshop "Nu merical Challenges in Lattice...

Reliable computing techniques are essential if the validity of the output of a - merical algorithm is to be guaranteed to be correct. Our society relies more and more on computer systems. Usually, our systems appear to work successfully, but there are sometimes serious, and often minor, errors. Validated computing is one essential technology to achieve increased software reliability. Formal - gor in the de?nition of data types, the computer arithmetic, in algorithm design, and in program execution allows us to guarantee that the stated problem has (or does not have) a solution in an enclosing...

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,...