The Lanczos method of Cullum and Willoughby is studied for euclidean Wilson fermions in quenched and unquenched SU(2) gauge elds on lattices of volume ranging from 4 4 to 16 4. The method is reliable even on larger lattices, but its cost for the computation of a given fraction of the spectrum grows (approximately) with the square of the lattice volume. We… (More)
Practical modifications of deterministic multigrid and conventional relaxation algorithms are discussed. New parameters need not be tuned but are determined by the algorithms themselves. One modification can be thought of as " updating on a last layer consisting of a single site ". It eliminates critical slowing down in computations of bosonic and fermionic… (More)
Complete spectra of the staggered Dirac operator 6 D are determined in four-dimensional SU(2) gauge elds with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient algorithms for propagators with the distribution of the eigenvalues of 6 D.
Recently, Kalkreuter obtained complete Dirac spectra for SU (2) lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as 12 4. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the… (More)
Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's and Willoughby's variant of the Lanczos method (whose convergence behaviour is closely linked with the local spectral… (More)
A Dirac choice for the averaging kernel C is implemented numerically. This improved kernel will be needed in gauge covariant multigrid computations for propagators of staggered fermions. Results for C and the variational coarse grid operator will be given in 2-d SU(2) gauge elds. C++ is advocated for future algorithm development. Big eeorts have been… (More)
EEective eld theories encode the predictions of a quantum eld theory at low energy. The eeective theory has a fairly low ultraviolet cutoo. As a result, loop corrections are small, at least if the eeective action contains a term which is quadratic in the elds, and physical predictions can be read straight from the eeective Lagrangean. Methods will be… (More)
We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge elds, no matter how strong the disorder, but one needs to introduce a \neural computations" point of view into large scale simulations: First, the system must learn how to do the simulations eeciently, then do the simulation (fast). The method… (More)