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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: