public static s19aa( x, out ifail )
|Visual Basic (Declaration)|
Public Shared Function s19aa ( _ x As , _ < > ByRef ifail As _ ) As
public: static s19aa( x, [ ] % ifail )
static member s19aa : x: * ifail: byref ->
On entry: the argument of the function.
On exit: unless the method detects an error (see [Error Indicators and Warnings]).
s19aa evaluates an approximation to the Kelvin function .
Note: , so the approximation need only consider .
The method is based on several Chebyshev expansions:
where , ,
and , , , and are expansions in the variable .
When is sufficiently close to zero, the result is set directly to .
For large , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner; therefore the method must fail.
Errors or warnings detected by the method:
Since the function is oscillatory, the absolute error rather than the relative error is important. Let be the absolute error in the result and be the relative error in the argument. If is somewhat larger than the machine precision, then we have:
(provided is within machine bounds).
For small the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision.
For medium and large , the error behaviour is oscillatory and its amplitude grows like . Therefore it is not possible to calculate the function with any accuracy when . Note that this value of is much smaller than the minimum value of for which the function overflows.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.