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Iteration procedures with incomplete corrections and solution of nonlinear equations. (English. Russian original) Zbl 0919.65035
Autom. Remote Control 58, No. 8, Pt. 1, 1285-1293 (1997); translation from Avtom. Telemekh. 1997, No. 8, 46-56 (1997).
Summary: Different iteration algorithms of the classical Gauss-Seidel method of numerically solving nonlinear vector equations are elaborated within the framework of the theory of dynamical systems with incomplete corrections. Some of these algorithms were studied earlier for special classes of equations. The results of this paper are theorems concerning the asymptotic stability of the equilibrium states of new classes of nonlinear dynamical systems.
65H10 Numerical computation of solutions to systems of equations
37-XX Dynamical systems and ergodic theory
65L07 Numerical investigation of stability of solutions
34D05 Asymptotic properties of solutions to ordinary differential equations