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Aug 12, 2011 at 1:29 comment added Robert Israel You might map these to uniformly spaced abscissas by the transformation $t = \sqrt{x^2/\delta^2 - a}$.
Aug 11, 2011 at 20:09 comment added jackj @J. M. : sorry for the long delay in responding. My abscissas look like $\delta\sqrt{a+n^2}$ where $a$ is "small" and $n$ is an integer.
Aug 7, 2011 at 9:28 comment added J. M. isn't a mathematician @jackj: Right, so probably we could give better suggestions if you'd mention what those "fixed abscissas" look like...
Aug 5, 2011 at 18:19 comment added jackj @Robert Israel: the problem I was trying to solve is precisely as you stated it. Thanks for the answer. So, essentially, many small-power polynomials are better than one large-power polynomial. What I plan to do is use the algorithm J.M. mentioned in each subinterval.
Aug 5, 2011 at 18:17 vote accept jackj
Aug 5, 2011 at 0:16 history answered Robert Israel CC BY-SA 3.0