A particular use of e02rbf is to compute values of the Padé approximants determined by e02raf.
Conte S D and de Boor C (1965) Elementary Numerical Analysis McGraw–Hill
Peters G and Wilkinson J H (1971) Practical problems arising in the solution of polynomial equations J. Inst. Maths. Applics.8 16–35
1: – Real (Kind=nag_wp) arrayInput
On entry: , for , must contain the value of the coefficient in the numerator of the rational function.
2: – IntegerInput
On entry: the value of , where is the degree of the numerator.
3: – Real (Kind=nag_wp) arrayInput
On entry: , for , must contain the value of the coefficient in the denominator of the rational function.
if , .
4: – IntegerInput
On entry: the value of , where is the degree of the denominator.
5: – Real (Kind=nag_wp)Input
On entry: the point at which the rational function is to be evaluated.
6: – Real (Kind=nag_wp)Output
On exit: the result of evaluating the rational function at the given point .
7: – IntegerInput/Output
On entry: ifail must be set to , . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value is recommended. If the output of error messages is undesirable, then the value is recommended. Otherwise, if you are not familiar with this argument, the recommended value is . When the value is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
The rational function is being evaluated at or near a pole.
when (so the denominator is identically zero).
An unexpected error has been triggered by this routine. Please
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.
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.
Parallelism and Performance
e02rbf is not threaded in any implementation.
The time taken is approximately proportional to .
This example first calls e02raf to calculate the Padé approximant to , and then uses e02rbf to evaluate the approximant at .