NAG Library Routine Document

E02RBF

1: $A (IA)$ – REAL (KIND=nag_wp) arrayInput: On entry: $A (j + 1)$ , for $j = 1, 2, \dots, l + 1$ , must contain the value of the coefficient $a_{j}$ in the numerator of the rational function.
2: $IA$ – INTEGERInput: On entry: the value of $l + 1$ , where $l$ is the degree of the numerator.

Constraint: $IA \geq 1$ .
3: $B (IB)$ – REAL (KIND=nag_wp) arrayInput: On entry: $B (k + 1)$ , for $k = 1, 2, \dots, m + 1$ , must contain the value of the coefficient $b_{k}$ in the denominator of the rational function.

Constraint: if $IB = 1$ , $B (1) \neq 0.0$ .
4: $IB$ – INTEGERInput: On entry: the value of $m + 1$ , where $m$ is the degree of the denominator.

Constraint: $IB \geq 1$ .
5: $X$ – REAL (KIND=nag_wp)Input: On entry: the point $x$ at which the rational function is to be evaluated.
6: $ANS$ – REAL (KIND=nag_wp)Output: On exit: the result of evaluating the rational function at the given point $x$ .
7: $IFAIL$ – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$: The rational function is being evaluated at or near a pole.

$IFAIL = 2$

On entry,	$IA < 1$ ,
or	$IB < 1$ ,
or	$B (1) = 0.0$ when $IB = 1$ (so the denominator is identically zero).

$IFAIL = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.8 in the Essential Introduction for further information.

$IFAIL = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.7 in the Essential Introduction for further information.

$IFAIL = - 999$: Dynamic memory allocation failed.
See Section 3.6 in the Essential Introduction for further information.

7 Accuracy

A running error analysis for polynomial evaluation by nested multiplication using the recurrence suggested by Kahan (see Peters and Wilkinson (1971)) is used to detect whether you are attempting to evaluate the approximant at or near a pole.