NAG Library Function Document
nag_kelvin_ker (s19acc) returns a value for the Kelvin function .
||nag_kelvin_ker (double x,
nag_kelvin_ker (s19acc) evaluates an approximation to the Kelvin function .
The function is based on several Chebyshev expansions.
For large , is so small that it cannot be computed without underflow and the function evaluation fails.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
x – doubleInput
On entry: the argument of the function.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
is too large, the result underflows and the function returns zero.
On entry, x
must not be less than or equal to 0.0:
The function is undefined and returns zero.
Let be the absolute error in the result, be the relative error in the result and be the relative error in the argument. If is somewhat larger than the machine precision, then we have , .
For very small , the relative error amplification factor is approximately given by , which implies a strong attenuation of relative error. However, in general cannot be less than the machine precision.
For small , errors are damped by the function and hence are limited by the machine precision.
For medium and large , the error behaviour, like the function itself, is oscillatory, and hence only the absolute accuracy for the function can be maintained. For this range of , the amplitude of the absolute error decays like which implies a strong attenuation of error. Eventually, , which asymptotically behaves like , becomes so small that it cannot be calculated without causing underflow, and the function returns zero. Note that for large the errors are dominated by those of the math library function exp.
Underflow may occur for a few values of
close to the zeros of
, which causes a failure NE_REAL_ARG_GT
The following program reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s19acce.c)
9.2 Program Data
Program Data (s19acce.d)
9.3 Program Results
Program Results (s19acce.r)