NAG Library Routine Document

C06BAF

1: SEQN – double precisionInput: On entry: the next term of the sequence to be considered.
2: NCALL – INTEGERInput/Output: On entry: on the first call NCALL must be set to 0. Thereafter NCALL must not be changed between calls.

On exit: the number of terms in the sequence that have been considered.
3: RESULT – double precisionOutput: On exit: the estimate of the limit of the sequence. For the first two calls, RESULT=SEQN .
4: ABSERR – double precisionOutput: On exit: an estimate of the absolute error in RESULT. For the first three calls, ABSERR is set to a large machine-dependent constant.
5: WORK(LWORK) – double precision arrayCommunication Array: Used as workspace, but must not be changed between calls.
6: LWORK – INTEGERInput: On entry: the dimension of the array WORK as declared in the (sub)program from which C06BAF is called.

Suggested value: (maximum number of terms in the sequence)+6 . See Section 8.2.
Constraint: LWORK≥7 .
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.

On exit: IFAIL=0 unless the routine detects an error (see Section 6).
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.

6 Error Indicators and Warnings

If on entry IFAIL=0 or -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: On entry, NCALL<0.

IFAIL=2: On entry, LWORK<7.

The accuracy of the absolute error estimate ABSERR varies considerably with the type of sequence to which the routine is applied. In general it is better when applied to oscillating sequences than to monotonic sequences where it may be a severe underestimate.

8 Further Comments

8.1 Timing

The time taken is approximately proportional to the final value of NCALL.

8.2 Choice of LWORK

For long sequences, a ‘window’ of the last n values can be used instead of all the terms of the sequence. Tests on a variety of problems indicate that a suitable value is n=50 ; this implies a value for LWORK of 56. You are advised to experiment with other values for your own specific problems.