NAG Library Routine Document

E02ACF

The routine also returns a number whose absolute value is the final reference deviation (see Section 6). The routine is an adaptation of Boothroyd (1967).

4 References

Boothroyd J B (1967) Algorithm 318 Comm. ACM 10 801

Stieffel E (1959) Numerical methods of Tchebycheff approximation On Numerical Approximation (ed R E Langer) 217–232 University of Wisconsin Press

5 Parameters

1: $X (N)$ – REAL (KIND=nag_wp) arrayInput: On entry: the values of the $x$ coordinates, $x_{i}$ , for $i = 1, 2, \dots, n$ .

Constraint: $x_{1} < x_{2} < \dots < x_{n}$ .
2: $Y (N)$ – REAL (KIND=nag_wp) arrayInput: On entry: the values of the $y$ coordinates, $y_{i}$ , for $i = 1, 2, \dots, n$ .
3: $N$ – INTEGERInput: On entry: the number $n$ of data points.
4: $A (M1)$ – REAL (KIND=nag_wp) arrayOutput: On exit: the coefficients $a_{i}$ of the final polynomial, for $i = 1, 2, \dots, m + 1$ .
5: $M1$ – INTEGERInput: On entry: $m + 1$ , where $m$ is the order of the polynomial to be found.

Constraint: $M1 < \min (N, 100)$ .
6: $REF$ – REAL (KIND=nag_wp)Output: On exit: the final reference deviation (see Section 6).

6 Error Indicators and Warnings

If an error is detected in an input parameter E02ACF will act as if a soft noisy exit has been requested (see Section 3.3.4 in the Essential Introduction).

7 Accuracy

This is wholly dependent on the given data points.

8 Parallelism and Performance

E02ACF is not threaded by NAG in any implementation.

E02ACF makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.