When sampling the distribution P(<(phi)over right arrow>)proportional to exp(-\A<(phi)over right arrow>\(2)), a global heat bath normally proceeds by solving the linear system A<(phi)over right arrow> = <(eta)over right arrow>, where <(eta)over right arrow> is a normal Gaussian vector, exactly. This paper shows how to preserve the distribution P(<(phi)over right arrow>) while solving the linear system with arbitrarily low accuracy. Generalizations are presented. [S1063-651X(99)13303-8].