The Method Of CGS And Smoothing CGS

The CGS method is one of the important method for solving large sparse systems.The amount of computational work and the memory space are small,but it may lead toa rather irregular convergence behaviour. The QMRCGS method is proposed in thispaper. The CSCGS method improves the problem about pivot breaking down on thebasis of CGS ,and it is a used method for solving large sparse systems. But it has thesame irregular convergence behaviour as CGS. The new method of MRS-CSCGS isproposed to deal with the problem above in the paper. Numerical experiments indicate that the new methods improve the convergenceproperty and discrease considerably computation time.