58 J.Zhoo Appl.Muth.Comput.92 (1998:49 5& Table 2 The result of Example 2 Order Algorithm 2 Gauss elimination U Flops Norm (- Flops Norm (-x 10 10 3998 6.7242×108 8207 1.8781×101日 20 10 11533 2.5209×101 24125 1.0121×100 30 20 50321 5.2676×100 10187 1.9155×10" 50 30 18938 6.3810×109 384447 1.3570×10" 50 40 267548 8.712s×109 540643 8.1077×10“ 50 50 344524 1.0074×10s 733965 1.5418×0× The Gauss elimination is provided by MATLAB. where: R=2,-m+从1=n From the above result we can see that the generalized (holesky method pre- sented in this paper will be efficient enough also for practical application.In fact,it would be still efficient when C=0 in linear systems (1)or (11). References [1]R.E.Bank.B.D.Welfert.H.Yserentant.A class of iterative methods for solving saddle point problems.Numer.Math.56 (1990)645 666. [2]A.Bjorck.Least squares methods.in:P.G.Ciarlet.J.L.Lions (Eds.)Handbook of Numerical Analysis vol.I:Solution of Equations in R".Elsevier.Amsterdam.1990. [3]J.H.Bramble.J.E.Pasciak.A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems.Math.Comp.50 (1988)I 17. [4]H.C.Elmain.G.H.Golub.Inexaet and preconditioned Uzawa algorithms for saddle point problems.Technical Report NA-93-012.Computer Science Depariment.Stanford University. 1993. [5]G.H.Golub.C.F.Van Loan.Matrix Computations.2nd ed..The Johns Hopkins University Press.Baltimore.1989. [6]G.H.Golub.M.L.Overton.The convergence of inexact Chebyshe and Richardson iterative methods for solving linear systems.Numer.Math.53 (1988)571 593. [7]1.Gustafsson.A class of first order factorizations.BIT 18 (1978)142 156. [8]Y.Yuan.Numerical methods for nonlinear programming.Modern Mathematics Series. Shanghai Scientific and Technical Publishers.1993