e02ajf
e02ajf
© Numerical Algorithms Group, 2002.
Purpose
E02AJF Integral of fitted polynomial in Chebyshev series form
Synopsis
[aint,ifail] = e02ajf(xmin,xmax,a<,qatm1,ifail>)
Description
This routine forms the polynomial which is the indefinite
integral of a given polynomial. Both the original polynomial and
its integral are represented in Chebyshev-series form. If
supplied with the coefficients a , for i=0,1,...,n, of a
i
polynomial p(x) of degree n, where
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
1 _ _
q(x)= -a' +a' T (x)+...+a' T (x),
2 0 1 1 n+1 n+1
and
/
q(x)= |p(x)dx.
/
_
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 integral to be with respect to the
_
variable x. If the integral with respect to x is required, set
x =1 and x =-1.
max min
Values of the integral can subsequently be computed, from the
coefficients obtained, by using E02AKF.
Parameters
e02ajf
Required Input Arguments:
xmin real
xmax real
a (:) real
Optional Input Arguments: <Default>
qatm1 real 0
ifail integer -1
Output Arguments:
aint (:) real
ifail integer