On the restrictively preconditioned conjugate gradient method for solving saddle point problems. Issue 1 (2nd January 2016) - Peng, Xiao-Fei; Li, Wen
Abstract : Bai et al. [2003, IMA J Numer. Anal. 23, 561–580] proposed the restrictively preconditioned conjugate gradient (RPCG) method. In this paper, based on the special structure of saddle point systems, we consider the RPCG method and propose a new format. This new format can be obtained by applying the classical PCG method to a simpler system instead of the original format, which greatly reduces computational cost. The new format of the RPCG method can often attain almost the same convergence rate as the original one. In particular, for some practical problems, the former converges faster than the latter. Numerical experiments show the efficiency of the proposed format.