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).