ELo ELSEVIER Applied Mathematics and Computation 92(1998)49 58 The generalized Cholesky factorization method for saddle point problems Jinxi Zhao Department of Mathematics. Nanjing Unicersity. Nanjing 210 008. China Abstract Over the past 10 years. a variety of iterative methods for saddle point problems have been proposed. In this paper, we present a class of direct methods, the so-called gener- alized Cholesky factorization method. for solving linear systems arising from saddle point problems or discretization of the Stokes equations. Numerical results illustrate the efficiency of new methods given in this paper. 1998 Elsevier Science Inc. All rights reserved. Keywords: Saddle point problem: Generalized Cholesky factorization: Condition I: Generalized positive definite 1.Introduction Consider the linear system of equations )-( where A is symmetric positive definite, B of full row rank, and C symmetric positive semi-definite. Problems in this class arise frequently in the context of minimization of quadratic forms subject to linear constraints [8]. An important example arises from the numerical discretization of the Stokes equations. In particular, we are concerned with the discretization of Project supported by the Science Foundation of the State Education Commission of China and the "863" plan of China. 0096-3003/98/S19.00 1998 Elsevier Science Inc. All rights reserved. PII: S0096-3003(97)10040-6