PADE APPROXIMATION BY RATIONAL FUNCTION 129
We can apply this formula to get the polynomial approximation directly for
a given function f (x), without having to resort to the Lagrange or Newton
polynomial. Given a function, the degree of the approximate polynomial, and the
left/right boundary points of the interval, the above MATLAB routine “cheby()”
uses this formula to make the Chebyshev polynomial approximation.
The following example illustrates that this formula gives the same approximate
polynomial function as could be obtained by applying the Newton polynomial
with the Chebyshev nodes.