NAG Library Function Document

nag_1d_ratnl_eval (e01rbc)

. 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: m – IntegerInput: On entry: $m$ , the number of terms in the continued fraction.
Constraint: $m \geq 1$ .
2: a[m] – const doubleInput: On entry: $a [j - 1]$ must be set to the value of the parameter $a_{j}$ in the continued fraction, for $j = 1, 2, \dots, m$ .
3: u[m] – const doubleInput: On entry: $u [j - 1]$ must be set to the value of the parameter $u_{j}$ in the continued fraction, for $j = 1, 2, \dots, m - 1$ . (The element $u [m - 1]$ is not used).
4: x – doubleInput: On entry: the value of $x$ at which the continued fraction is to be evaluated.
5: f – double *Output: On exit: the value of the continued fraction corresponding to the value of $x$ .
6: fail – NagError *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 $R (x)$ , 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

a_{j}

and

u_{j}

of a continued fraction (as determined by the example for nag_1d_ratnl_interp (e01rac)) and evaluates the continued fraction at a point

x

NAG Library Function Documentnag_1d_ratnl_eval (e01rbc)

+− Contents

1 Purpose

2 Specification

3 Description