. 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 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
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

nag_1d_ratnl_eval (e01rbc) is not threaded in any implementation.

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

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_1d_ratnl_eval (e01rbc)