50 .wf,.1th.(au.2190g)495N -A4-下pf. Vu -0).on 2. 4=0.oni2. (2) /P=0 where is a simply connected bounded domain in R.s==2 or 3.This system of the Stokes equations is a fundamental problem arising in computational fluid dynamics [4].Discretization of Eq.(2)by finite difference or finite element techniques leads to a linear system of equations of (1). In recent years.a variety of iterative algorithms have been devised for solving saddle point problems [1.3.4.6.7].In this paper.we have developed the generalized Cholesky factorization for four typical matrices arising in numerical optimization and computational fluid dynamics.Using the matrix factorization.we establish a class of direct methods for solving the corre- sponding linear system.New methods proposed in this paper remain main advantages of the classical Cholesky factorization for positive definite sys- tems.Hence the new method is referred to as the generalized Cholesky fac- torization method. In the following we always assume that matrices 4E R"".BR",and C"satisly the following condition. Condition I.A is symmetric positive definite.B is of full row rank and C is symmetrie semi-positive definite. 2.Symmetric indefinite case Let us assume that G is an (m+n)*(m+n)matrix and express it as 3 where A.B and C satisfy Condition I.It is easy to see that G is symmetric in- definite.The purpose of this section is based on the matrix factorization of G to give a new algorithm for solving the linear system (1). Firstly.we can prove the following theorem. Theorem 1.Ler G he an (m+*im+n)matrix expressed hy Ey.(3)and A.B.C sutisfr Condition I.Then there ahuvs exists the factorizution form G=B B (4)