Version 3 (modified by sam, 11 years ago) (diff)

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# Remez tutorial 5/5: additional tips

This part of the tutorial is constantly updated. Check its history to know what is new.

## When not to use Remez?

There are cases when you should expect the Remez algorithm to potentially perform badly:

There are cases where you should not try to use the Remez algorithm at all:

• when the range is not finite, eg. [0,+∞]
• when the function to approximate has an infinite derivative at a point contained in or near the approximation range, eg. sqrt(x) or cbrt(x) in 0

## What if I want to use Remez anyway?

If you need to approximate a function f(x) over [a,+∞] and for some reason you want to use the Remez exchange algorithm, you can still through a change of variable: y = 1/x. The function to approximate becomes f(1/y) and the new range is [0,1/a] (see “changing variables” for how to deal with 1/x in 0. Your minimax polynomial will use 1/x as its variable; please be aware that computing 1/x at runtime may be expensive.