Algorithms Defined by Nash Iteration: Some Implementations via Multilevel Collocation and Smoothing

By: Gregory E. Fasshauer, Eugene C. Gartland, Jr. and Joseph W. Jerome

We describe Nash iteration in numerical analysis, as applied to the solution of linear differential equations. We employ an adaptation involving a splitting of the inversion and the smoothing into two separate steps. We had earlier shown how these ideas apply to scattered data approximation. In this work, we review the ideas in the context of the general nonlinear problem, before proceeding to a detailed set of simulation examples for the linear problem, primarily involving collocation and radial basis functions. We make use of approximate smoothers, involving the solution of evolution equations with calibrated time steps.
This paper appeared in J. Computational and Applied Mathematics 119 (2000), 161--183 and can be viewed in the following format: