J.Zhuo Appl.Math.('omput.93 1998.49 58 55 Since the realization procedures of submatrices L.La and L,are the same as in Section 2.Hence we can propose an algorithm for solving the linear system Algorithm 2. 1.Given 4=lanER".B=huR"xm and C'=cul E R""satisfying Condition I and given f∈R".g∈R" 2.L=]=chol(4)or using expression (7). 3.ComputingL=gl from Ll.B or using expression (8). 4.L=[r=chol(C+LaL)or using expression (9). 5.Computing =( from ())(） 6.Obtained the final solution of'the linear system (1)from (:）)() Consider the special case where C=0 in Eq.(12).i.e.. Obviously.we can prove the following Theorem 4./f G= und A.B sutisfr Condition 1.then we hate Ga =LaL. 14) 17r 4-(伦2)=（日） Here matrices L and L&are the same as in Theorem 3.and L-is the Cholesky fac- tor ofL Since L is of full row rank.there always exists the Cholesky factor L. of LaLk