D02UAF obtains the Chebyshev coefficients of a function discretized on Chebyshev Gauss–Lobatto points. The set of discretization points on which the function is evaluated is usually obtained by a previous call to
D02UCF.
D02UAF computes the coefficients
cj, for
j=1,2,…,n+1, of the interpolating Chebyshev series
which interpolates the function
fx evaluated at the Chebyshev Gauss–Lobatto points
Here
Tjx- denotes the Chebyshev polynomial of the first kind of degree
j with argument
x- defined on
-1,1. In terms of your original variable,
x say, the input values at which the function values are to be provided are
where
b and
a are respectively the upper and lower ends of the range of
x over which the function is required.
Canuto C, Hussaini M Y, Quarteroni A and Zang T A (2006)
Spectral Methods: Fundamentals in Single Domains Springer
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The Chebyshev coefficients computed should be accurate to within a small multiple of machine precision.