Parallel Algorithms

Abstract

In the previously considered relaxation algorithms, current configurations were updated sequentially: The Gibbs sampler (possibly) changed a given configuration x in a systematically or randomly chosen site s, replacing the old value x _s by a sample y _s from the local characteristic П(x _s |x_S\{s}) The next step started from the new configuration y = y _s x _{S \{s}}. More generally, on a (random) set A ⊂ S the subconfiguration x _A could be replaced by a sample from П(y _A |x _{S \A}) and the next step started from y = y _A x _{S \A}. The latter reduces the number of steps needed for a good estimate but in general does not result in a substantial gain of computing time. The computational load in each step increases as the subsets get larger; for large A (A = S) the algorithms even become computationally infeasible.