Chebyshev Approximation (Not in Base Package)

Determines a given function using Chebyshev polynomials. Details

number of points is the number of equidistant points in the interval (start,end). The default is 10.
start is the start point of the interval. The default is 0.0.
end is the end point of the interval. The default is 1.0.
order is the degree of the Chebyshev approximation. The degree is the number of different Chebyshev polynomials

describing the formula. The default is 3.

formula is a string describing the function under investigation. The Formula VIs check the syntax of this string.
C is an array of coefficients belonging to

X is the x values dividing (start,end) in equidistant subintervals.
Y is the y values of the Chebyshev polynomial at points X.
error returns any error or warning condition from the VI.

Chebyshev Approximation Details

Let n be a given natural number. The function f(x) can approximately be represented by

where

are the first Chebyshev polynomials. The can be calculated as sums of the form

where

for

k = 1, ..., n.