-- Polynomial approximation for 1/(x+a) in large domain.

Hi

I would like to approximate the function 1/(x+a) (for a constant a) in
a large domain. I tried to minimize the L-infinity norm of the error
over my domain (I was working on a discrete version of the problem,
with irregular sampling over the domain, based on the regions that
were of more importance to me - I guess I could do a weighting as
well, but I couldn't figure out how...).

I found that so long as a is a decade less than the supremum of x, I
can get a fairly good approximation. But once x gets closer to a, the
approximation becomes lousy and if x>a, I get very very bad results.
Scaling x would obviously not work well here. I would like to know
what other approximation would be suitable - I'd rather not use a
rational approximation, since I start am approximating a rational
function. Would another norm be any better? Is there any other basis
that could approximate 1/(x+a) over a large domain?

Also, I am not doing this for interpolation - so I can't break it up
into subdomains and run it - the application is for control systems,
and I need a single polynomial for the entire domain.

Any suggestions, or references, would be appreciated - I have
absolutely no idea how to proceed!!!

Thanks
Srikanth
.

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