56 .Zhuw/1ppl.Mh.C.921199然！495 4.Discussion The method described in this paper retains the main advantages of the clas- sical Cholesky factorization.During the course of the computation.N =m+n square roots must be taken.Condition I assures us that the arguments of these square roots will be positive.About N/6 flops are needed beyond n square roots.Finally.because 4 is symmetric positive definite,the elements of L will be controllable.In fact,we have the following relation, 1a≤a.i=1:m.k=1:i (15) Since L8=B(LI). it follows that ca+ If we take M=,max（g+·+gim) 5成 then ≤cw+M.i=1:n.j=1:i. That is,the elements of L (or Ly.L.L:cannot become too large. 5.Numerical results We now present the results of numerical experiments for solving Eqs.(1) and (11).All experiments were performed in MATLAB on a PC-386 computer. Take Am=a=Hn+Inm∈Rm" where Hm= [1 i+i-1 is an m x m Hilbert matrix and/is an m x m unit matrix. Also take B=h,l=maxi.i川∈R"m and Cw=c=UG,U∈R