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Undoubtedly0
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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
[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.
[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
Code:
>> x = 0.9;
>> p60 = ChebyshevPoly(60);
>> polyval(p60,x)
ans =
-1.4447e+04
where ChebyshevPoly() comes from mathworks.com.