On the optimization of a class of algorithms for solving nonsymmetric saddle point problems

To solve a nonsingular nonsymmetric system of linear equations with a saddle point, an algorithm with three constant iteration parameters is developed as an extension of the well-known Arrow–Hurwicz algorithm. An estimate for the spectral radius of the transition operator is derived. The asymptotic convergence rate is examined as a function of the nonsymmetric part of the original problem. The results of numerical experiments are presented.