e02aef

Purpose

Synopsis

[p,ifail] = e02aef(a,xcap<,ifail>)

Description

 
 This routine evaluates the polynomial
 
               1     _       _       _             _
               -a T (x)+a T (x)+a T (x)+...+a   T (x)
               2 1 0     2 1     3 2         n+1 n  
 
                  _                _             _             
 for any value of x satisfying -1<=x<=1. Here T (x) denotes the 
                                               j               
 Chebyshev polynomial of the first kind of degree j with argument 
 _                                      
 x. The value of n is prescribed by the user.
 
                           _                                     
 In practice, the variable x will usually have been obtained from 
 an original variable x, where x   <=x<=x    and
                                min      max 
 
                         ((x-x   )-(x   -x))
                      _       min    max
                      x= -------------------
                             (x   -x   )
                               max  min
 
 Note that this form of the transformation should be used 
 computationally rather than the mathematical equivalent
 
                            (2x-x   -x   )
                         _       min  max
                         x= --------------
                             (x   -x   )
                               max  min
 
                                                        _        
 since the former guarantees that the computed value of x differs 
 from its true value by at most 4(epsilon), where (epsilon) is the
 machine precision, whereas the latter has no such guarantee.
 

Parameters

e02aef

Required Input Arguments:

a (:)                                 real
xcap                                  real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

p                                     real
ifail                                 integer