15 digit accuracy

Abstract

The code AIGAU15.FOR produces a 15 digit Aigau by integrating from values calculated by code in int15.zip

Introduction:

For z < -3, it was established in ../aiglz/Welcome.htm that Gauss Laguerre integration produces 15 digit accuracy. The code in this part of the function simply removes the doubling of the integration used to determine accuracy.

The file AIGAUL.IN was generated by code in aiglz.zip which simply integrates from - ¥ to six.

The code AIGAU15.FOR uses Aigau(x)=1-Aigau(-x) for values > 0.

Figure 1 log(Aigau15) – Aigaul taigaul.for

Figure 2 Large z limit

Note that the full integration ends with a value of +1.77 E-15, while the subtraction of the low limit ends with nearly 0.

Figure 3 AiGauss(z) on a log scale - black 0, abs (exp(aigaul)-aigau) – blue

Below -3 the algorithms are the same for each point calculated. Above zero they are quite different.