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Topic: Chebyshev polynomials derivative
Replies: 1   Last Post: Aug 18, 2014 10:31 AM

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Cristiano

Posts: 60
Registered: 12/7/12
Chebyshev polynomials derivative
Posted: Aug 18, 2014 9:16 AM
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I found the C source code to interpolate a set of points using the
Chebyshev polynomials:
http://people.sc.fsu.edu/~jburkardt/c_src/chebyshev/chebyshev.html
the file is chebyshev.c.

I need to calculate also the derivative of the polynomial T(N,X).

I found the formulas for that, but unfortunately the algorithm used in
the program to calculate T(N,X) is not clear to me, so I'm not able to
calculate the derivative.

This is the algorithm (in pseudo-code):

[a,b] is the interpolation interval
x is the independent variable
c(i) are the coefficients

dip1 = 0
di = 0
y = ( 2 * x - a - b ) / ( b - a )
for i = n - 1 to 1:
dip2 = dip1
dip1 = di
di = 2 * y * dip1 - dip2 + c(i)
end for
T(N,X)= y * di - dip1 + c(0) / 2

Please, could somebody tell me how to calculate the derivative?

Thank you
Cristiano



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