NAG Library Routine Document

D02UCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: $n$, where the number of grid points is $n+1$. This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.

Constraint: $\mathbf{N}>0$ and N is even.

2:     A – REAL (KIND=nag_wp)Input

On entry: $a$, the lower bound of domain $\left[a,b\right]$.

Constraint: $\mathbf{A}<\mathbf{B}$.

3:     B – REAL (KIND=nag_wp)Input

On entry: $b$, the upper bound of domain $\left[a,b\right]$.

Constraint: $\mathbf{B}>\mathbf{A}$.

4:     X($\mathbf{N}+1$) – REAL (KIND=nag_wp) arrayOutput

On exit: the Chebyshev Gauss–Lobatto grid points, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n+1$, on $\left[a,b\right]$.

5:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,

$\mathbf{N}\le 0$ or N is odd.

$\mathbf{IFAIL}=2$

On entry,

$\mathbf{A}\ge \mathbf{B}$.

7  Accuracy

8  Further Comments

9  Example