nag_1d_ratnl_eval (e01rbc) (PDF version)
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NAG 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
Rix=am-i+ 2x-um-i+ 1 1+Ri- 1x ,   for ​ i=m,m- 1,,2.
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

On entry, argument value had an illegal value.
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.
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  Parallelism and Performance

Not applicable.

9  Further Comments

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

10  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.

10.1  Program Text

Program Text (e01rbce.c)

10.2  Program Data

Program Data (e01rbce.d)

10.3  Program Results

Program Results (e01rbce.r)

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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014