nag_1d_ratnl_eval (e01rbc) (PDF version)
e01 Chapter Contents
e01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_1d_ratnl_eval (e01rbc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_1d_ratnl_eval (e01rbc) evaluates continued fractions of the form produced by nag_1d_ratnl_interp (e01rac).

2  Specification

#include <nag.h>
#include <nage01.h>
void  nag_1d_ratnl_eval (Integer m, const double a[], const double u[], double x, double *f, NagError *fail)

3  Description

nag_1d_ratnl_eval (e01rbc) evaluates the continued fraction
Rx=a1+Rmx
where
Rix=am-i+ 2x-um-i+ 1 1+Ri- 1x ,   for ​ i=m,m- 1,,2.
and
R1x=0
for a prescribed value of x. nag_1d_ratnl_eval (e01rbc) is intended to be used to evaluate the continued fraction representation (of an interpolatory rational function) produced by nag_1d_ratnl_interp (e01rac).

4  References

Graves–Morris P R and Hopkins T R (1981) Reliable rational interpolation Numer. Math. 36 111–128

5  Arguments

1:     mIntegerInput
On entry: m, the number of terms in the continued fraction.
Constraint: m1.
2:     a[m]const doubleInput
On entry: a[j-1] must be set to the value of the parameter aj in the continued fraction, for j=1,2,,m.
3:     u[m]const doubleInput
On entry: u[j-1] must be set to the value of the parameter uj in the continued fraction, for j=1,2,,m-1. (The element u[m-1] is not used).
4:     xdoubleInput
On entry: the value of x at which the continued fraction is to be evaluated.
5:     fdouble *Output
On exit: the value of the continued fraction corresponding to the value of x.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_POLE_PRESENT
x corresponds to a pole of Rx, or is very close. x=value.

7  Accuracy

See Section 7 in nag_1d_ratnl_interp (e01rac).

8  Further Comments

The time taken by nag_1d_ratnl_eval (e01rbc) is approximately proportional to m.

9  Example

This example reads in the arguments aj and uj of a continued fraction (as determined by the example for nag_1d_ratnl_interp (e01rac)) and evaluates the continued fraction at a point x.

9.1  Program Text

Program Text (e01rbce.c)

9.2  Program Data

Program Data (e01rbce.d)

9.3  Program Results

Program Results (e01rbce.r)


nag_1d_ratnl_eval (e01rbc) (PDF version)
e01 Chapter Contents
e01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012