Abstract
For a class of nonsingular saddle-point problems, Bai et al. in 2008 studied an efficient parameterized inexact Uzawa (PIU) method; see [Z.-Z. Bai, Z.-Q. Wang, On parameterized inexact Uzawa methods for generalized saddle-point problems, Linear Algebra Appl. 428 (2008) 2900---2932]. In this paper, we use a generalized version of the PIU method, named as generalized PIU (GPIU) method, to solve the singular saddle-point problems. The semi-convergence properties of the GPIU method are derived under suitable restrictions on the involved iteration parameters. Moreover, the quasi-optimal iteration parameters and the corresponding quasi-optimal semi-convergence factor are also determined. Numerical experiments are used to verify the feasibility and effectiveness of the GPIU method.
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