Subspace selection algorithms to be used with the nonlinear projection methods in solving systems of nonlinear equations

AbstractThe nonlinear projection methods are minimization procedures for solving systems of nonlinear equations. They permit reevaluation of nk, 1 ≤ nk ≤ n, components of the approximate solution vector at each iteration step where n is the dimension of the system. At iteration step k, the reduction in the norm of the residue vector depends upon the nk components which are reevaluated. These nk components are obtained by solving a linear system.We present two algorithms for determining the components to be modified at each iteration of the nonlinear projection method and compare the use of these algorithms to Newton's method. The computational examples demonstrate that Newton's method, which reevaluates all components of the approximate solution vector at each iteration, can be accelerated by using the projection techniques