The Calibration of Discretization and Iteration in Nonlinear Approximation
Abstract
The solution of nonlinear problems, formulated as fixed point
problems, requires a combination of iteration and discretization. Some
of the most effective strategies are successive approximation, Newton
iteration, and Nash iteration. The mathematical framework required to
illustrate the first two of these will be described in terms of the
specific example of the two-point boundary value problem for the
undamped, oscillating pendulum. Some remarks will also be made for
Nash iteration, which is a modified Newton iteration with smoothing.
