## Method of Precision Increase by Averaging with Application to Numerical Differentiation

**Authors:** Andrej Liptaj

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution, interpreted as the value of the quantity of interest, can be determined with better precision than what is the precision provided by a single algorithm. Often, with lack of enough independent algorithms, one can proceed differently: many practical algorithms introduce a bias using a parameter, e.g. a small but finite number to compute a limit or a large but finite number (cutoff) to approximate infinity. One may vary such parameter of a single algorithm and interpret the resulting numbers as generated by several algorithms. A numerical evidence for the validity of this approach is shown for differentiation.

**Comments:** 19 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-06-13 05:25:56

**Unique-IP document downloads:** 10 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*