Projection methods were first introduced to solve systems of linear equations and have recently been extended to nonlinear problems. The basic idea behind the nonlinear projection methods is to minimize the square of the norm of the residue vector at each iteration step. These belong to the descent class of minimization methods. They are not strict total step methods and are used to change from 1 to n (n being the dimension of the nonlinear system of equations) components of the approximate solution vector at any given iteration step.nThe class of projection-based methods presented in this dissertation are total step methods. They change all n components of the approximate solution vector at every iteration. The main advantage of these methods over the basic projection methods is that both the residue vector and the Jacobian matrix of the nonlinear system need be evaluated only once per iteration cycle. In general, the rate of convergence of projection-based methods is faster than that of basic projection methods. Projection-based methods use less computational time and fewer number of cycles to reduce the norm of the residue to a given tolerance. Therefore, they could be considered as accelerations to basic projection methods.
展开▼
