Quasi-Newton methods for solving underdetermined nonlinear simultaneous equations

摘要

We analyze iterative processes of type xk+1 = xk − π(xk, Ek)F(xk) for solving F(x) = 0, F:Rn → Rm, m ≤ n. Parameters Ek are updated at each iteraction 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.