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