. nag_interp_1d_ratnl_eval (e01rb) is intended to be used to evaluate the continued fraction representation (of an interpolatory rational function) produced by nag_interp_1d_ratnl (e01ra).

References

Graves–Morris P R and Hopkins T R (1981) Reliable rational interpolation Numer. Math. 36 111–128

Parameters

Compulsory Input Parameters

1: $a (m)$ – double array: $a (j)$ must be set to the value of the parameter $a_{j}$ in the continued fraction, for $j = 1, 2, \dots, m$ .
2: $u (m)$ – double array: $u (j)$ must be set to the value of the parameter $u_{j}$ in the continued fraction, for $j = 1, 2, \dots, m - 1$ . (The element $u (m)$ is not used).
3: $x$ – double scalar: The value of $x$ at which the continued fraction is to be evaluated.

Optional Input Parameters

1: $m$ – int64int32nag_int scalar: Default: the dimension of the arrays a, u. (An error is raised if these dimensions are not equal.)
$m$ , the number of terms in the continued fraction.

Constraint: $m \geq 1$ .

Output Parameters

1: $f$ – double scalar: The value of the continued fraction corresponding to the value of $x$ .
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: The value of x corresponds to a pole of $R (x)$ or is so close that an overflow is likely to ensue.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

See Accuracy in nag_interp_1d_ratnl (e01ra).

Further Comments

The time taken by nag_interp_1d_ratnl_eval (e01rb) is approximately proportional to

m

Example

This example reads in the arguments

a_{j}

and

u_{j}

of a continued fraction (as determined by the example for nag_interp_1d_ratnl (e01ra)) and evaluates the continued fraction at a point

x

Open in the MATLAB editor: e01rb_example

function e01rb_example


fprintf('e01rb example results\n\n');

% Calculate rational approximation coefficients
x = [0:4];
f = [4   2   4   7   10.4];

[m, a, u, ifail] = e01ra( ...
                          x, f);

% Evaluate at single point
x = 6;
[f, ifail] = e01rb( ...
                    a, u, x, 'm', m);

fprintf('x    = %12.4e\n',x);
fprintf('R(x) = %12.4e\n',f);

e01rb example results

x    =   6.0000e+00
R(x) =   1.7714e+01

PDF version (NAG web site, 64-bit version, 64-bit version)

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