NAG FL Interface
e02alf (dim1_​minimax_​polynomial)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of data points.

Constraint: $\mathbf{n}\ge 1$.

2: $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

On entry: the values of the $x$ coordinates, $x_i$, for $\mathit{i}=1,2,\dots ,n$.

Constraint: $x_1<x_2<\cdots <x_n$.

3: $\mathbf{y}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input

On entry: the values of the $y$ coordinates, $y_i$, for $\mathit{i}=1,2,\dots ,n$.

4: $\mathbf{m}$ – Integer Input

On entry: $m$, where $m$ is the degree of the polynomial to be found.

Constraint: $0\le \mathbf{m}<\min \left(100,\mathbf{n}-1\right)$.

5: $\mathbf{a}\left(\mathbf{m}+1\right)$ – Real (Kind=nag_wp) array Output

On exit: the coefficients $a_i$ of the minimax polynomial, for $\mathit{i}=0,1,\dots ,m$.

6: $\mathbf{ref}$ – Real (Kind=nag_wp) Output

On exit: the final reference deviation, i.e., the maximum deviation of the computed polynomial evaluated at $x_{\mathit{i}}$ from the reference values $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. ref may return a negative value which indicates that the algorithm started to cycle due to round-off errors.

7: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

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

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=2$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}<100$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}<\mathbf{n}-1$.

$\mathbf{ifail}=3$

On entry, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{x}\left(\mathit{i}+1\right)=〈\mathit{\text{value}}〉$ and $\mathbf{x}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\left(\mathit{i}+1\right)>\mathbf{x}\left(\mathit{i}\right)$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results