Multistep Approximation Algorithms: Improved Convergence Rates through Postconditioning with Smoothing Kernels

By: Gregory E. Fasshauer and Joseph W. Jerome

We show how certain widely used multistep approximation algorithms can be interpreted as instances of an approximate Newton method. It is known that convergence rates of such Newton methods experience a "loss of derivatives". Smoothing, based upon Nash-Moser iteration, is introduced as a postconditioning step. Radial kernels and basis functions are employed.
This paper has appeared in Advances in Comp. Math. 10 (1999), 1--27, and can be viewed in the following format: