QUASI-NEWTON METHODS FOR SOLVING UNDERDETERMINED NONLINEAR SIMULTANEOUS-EQUATIONS

[摘要] We analyze iterative processes of type x(k+1) = x(k) - phi(x(k),E(k))F(x(k)) for solving F(x) = 0, F:R(n) --> R(m), m less-than-or-equal-to n. Parameters E(k) are updated at each iteration using least-change secant update procedures. We prove local, linear and superlinear convergence results. We introduce two new superlinearly convergent methods of this type, and one linearly convergent Quasi-Newton generalization of Cimmino's parallel algorithm for solving linear systems. Some numerical experiments are presented.

[发布日期] 1991-04-04

[关键词] NONLINEAR SYSTEMS;QUASI-NEWTON METHODS;LOCAL CONVERGENCE