Analysis of iterative algorithms of Uzawa type for saddle point problems Original Research Article

In this paper, we consider the convergence criteria for iterative algorithms of Uzawa type for solving linear saddle point problems. Theoretically weaker convergence criteria than before are established for the general case and these are used to deduce conditions for convergence of two special cases: the exact Uzawa algorithm and the linear one-step method. The conclusions given here hold for both symmetric and nonsymmetric saddle point problems. These new sufficient conditions are compared with some known results and illustrated by two examples. Numerical experiments to verify the conclusions in this paper for the preconditioned exact Uzawa algorithm are provided.