s19abc (pdf version)
Chapter Contents
Chapter Introduction
NAG C Library Contents

NAG C Library Function Document

nag_kelvin_bei (s19abc)

+ Contents

     1 Purpose
     2 Specification
     3 Description
     4 References
     5 Parameters
     6 Error Indicators and Warnings
     7 Accuracy
     8 Further Comments
+  9 Example

1  Purpose

nag_kelvin_bei (s19abc) returns a value for the Kelvin function beix .

2  Specification

#include <nag.h>
#include <nags.h>

void nag_kelvin_bei(double x, NagError *fail)

3  Description

nag_kelvin_bei (s19abc) evaluates an approximation to the Kelvin function beix .
The function is based on several Chebyshev expansions.
For large x , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner; therefore the function must fail.

4  References

5  Parameters

1:     x – double Input
On entry: the argument x  of the function.
2:     fail – NagError *Input/Output

6  Error Indicators and Warnings

NE_REAL_ARG_GT
On entry, x  must not be greater than value: x=value .
x  is too large for an accurate result to be returned and the function returns zero.

7  Accuracy

Since the function is oscillatory, the absolute error rather than the relative error is important. Let E  be the absolute error in the function, and δ  be the relative error in the argument. If δ  is somewhat larger than the machine precision , then we have E x - ber 1 x + bei 1 x / 2 δ  (provided E  is within machine bounds).
For small x  the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision.
For medium and large x , the error behaviour is oscillatory and its amplitude grows like x / 2 π e x / 2 . Therefore it is impossible to calculate the functions with any accuracy when x e x / 2 > 2π / δ . Note that this value of x  is much smaller than the minimum value of x  for which the function overflows.

8  Further Comments

None.

9  Example

The following program reads values of the argument x  from a file, evaluates the function at each value of x  and prints the results.

9.1  Program Text

9.2  Program Data

9.3  Program Results



© The Numerical Algorithms Group Ltd, Oxford, UK. 2004