Numer. Math. (1998) 79: 643–646 Numerische Mathematik c  Springer-Verlag 1998 Electronic Edition On an iterative method for saddle point problems ⋆ Zhanye Tong, Ahmed Sameh Department of Computer Science, Purdue University, West Lafayette, IN 47906, USA Received November 18, 1996 / Revised version received March 18, 1997 Summary. Convergence behavior of a nested iterative scheme presented in a paper by Bank, Welfert and Yserentant is studied. It is shown that this scheme converges under conditions weaker than that stated in their paper. Mathematics Subject Classification (1991): 15A57, 65N20 1 Introduction In this note, we consider a scheme proposed in [1] for the solution of linear equations  AB B T 0  x y  =  f g  (1.1) where A is a symmetric positive definite n × n matrix, B is an n × m matrix of maximal rank, m ≤ n. This scheme is a stationary Richardson iteration with a preconditioner ˆ M =  ˆ A B B T − ˆ G + B T ˆ A −1 B  (1.2) Here ˆ A and ˆ G are symmetric positive definite approximations of A and B T ˆ A −1 B, respectively. In [1], it is shown that under a specially introduced norm ‖| · ‖| (see [1], pp.654), the error propagation matrix I − ˆ M −1 M satisfies ‖|I − ˆ M −1 M ‖| ≤ max  α, 2β 1 − β  (1.3) ⋆ Research supported by NSF grants No. CCR-9396332 and CDA-9414015, and ARPA/NIST grant No. USDOC/60NANB4D1615 Numerische Mathematik Electronic Edition page 643 of Numer. Math. (1998) 79: 643–646