Effect of Rounding Error in CG Method with Reduction of Synchro. Point by Modification of Sequence of Its Algorithm

Abstract

  For gainging high speedup of Conjugate Gradient method on parallel computer, it is cricial to reduce the number of synchro. points which stem from the operation of inner point. Therefore, we consider on relationship between rounding error and CG method with reduction of the number of synchro. points in parallel computing. Through numerical experimnts, it turned out that CG method with reduction of the number of synchro. points by A. Chronopoulos is greatly affected by rounding error caused by finite floating-point arithmetics of inner products.