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
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