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