e02ahf
e02ahf
© Numerical Algorithms Group, 2002.
Purpose
E02AHF Derivative of fitted polynomial in Chebyshev series form
Synopsis
[patm1,adif,ifail] = e02ahf(xmin,xmax,a<,ifail>)
Description
This routine forms the polynomial which is the derivative of a
given polynomial. Both the original polynomial and its derivative
are represented in Chebyshev-series form. Given the coefficients
a , for i=0,1,...,n, of a polynomial p(x) of degree n, where
i
1 _ _
p(x)= -a +a T (x)+...+a T (x)
2 0 1 1 n n
_
the routine returns the coefficients a , for i=0,1,...,n-1, of
i
the polynomial q(x) of degree n-1, where
dp(x) 1_ _ _ _ _
q(x)= -----= -a +a T (x)+...+a T (x).
dx 2 0 1 1 n-1 n-1
_
Here T (x) denotes the Chebyshev polynomial of the first kind of
j
_
degree j with argument x. It is assumed that the normalised
_
variable x in the interval [-1,+1] was obtained from the user's
original variable x in the interval [x ,x ] by the linear
min max
transformation
2x-(x +x )
_ max min
x= --------------
x -x
max min
and that the user requires the derivative to be with respect to
_
the variable x. If the derivative with respect to x is required,
set x =1 and x =-1.
max min
Values of the derivative can subsequently be computed, from the
coefficients obtained, by using E02AKF.
Parameters
e02ahf
Required Input Arguments:
xmin real
xmax real
a (:) real
Optional Input Arguments: <Default>
ifail integer -1
Output Arguments:
patm1 real
adif (:) real
ifail integer