Prolegomena to any future computer evaluation of the QCD mass spectrum

In recent years we have seen many computer based evaluations of the QCD mass spectrum. At the present moment a reliable control of the systematic errors is not yet achieved; as far as the main sources of systematic errors are the non zero values of the lattice spacing and the finite size of the box, in which the hadrons are confined, we need to do extensive computations on lattices of different shapes in order to be able to extrapolate to zero lattice spacing and to infinite box. While it is necessary to go to larger lattices, we also need efficient algorithms in order to minimize the statistical and systematic errors and to decrease the CPU time (and the memory) used in the computation. In these lectures the reader will find a review of the most common algorithms (with the exclusion of the application to gauge theories of the hopping parameter expansion in the form proposed: it can be found in Montvay's contribution to this school); the weak points of the various algorithms are discussed and, when possible, the way to improve them is suggested. For reader convenience the basic formulae are recalled in the second section; in section three we find a discussion of finite volume effects, while the effects of a finite lattice spacing are discussed in section four; some techniques for fighting against the statistical errors and the critical slowing down are found in section five and six respectively. Finally the conclusions are in section seven