Hi all. I am trying to evaluate high-degree Chebyshev polynomials of the first kind. It is well known that for each Chebyshev polynomial [itex]T_n[/itex], if [tex]-1\le x\le1[/tex] then(adsbygoogle = window.adsbygoogle || []).push({});

[tex]-1\le T_n(x)\le 1[/tex]

However, when I try to evaluate a Chebyshev polynomial of a high degree, such as [itex]T_{60}[/itex], MATLAB gives results that do not stay within these bounds. I assume this is due to a lack of precision. Any suggestions?

As an example, try

where ChebyshevPoly() comes from mathworks.com.Code (Text):>> x = 0.9;

>> p60 = ChebyshevPoly(60);

>> polyval(p60,x)

ans =

-1.4447e+04

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# Evaluating high-degree polynomials

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