The construction of an algebraically reduced system for the acceleration of preconditioned conjugate gradients

In this paper we show how an algebraically reduced system can be constructed, for which the preconditioned conjugate gradient method converges faster than for the original system. For this method it is necessary that the original matrix is symmetric positive-definite. Our approach is based on an efficient projection on a well-chosen subspace and we show an application in which a cyclically reduced system is one step further reduced by this novel technique.