For example: percentage of error when Actual Value is 0 and Recorded Value is .1
This is not necessary that one should find relative and % error for very small values. They are important when your actual(exact) value is very large.
Sir, I am working on Finite Element Analysis for an aerospace company in USA.
The Company Spoke wants to get ma computed values sometimes validated by hand calculation. And sometimes the actual stress value may be zero. but the numerical analysis value varies by less than 1. And I was wondering how to make it in percentage. !
I try to follow. If you get experimental results which allow a statistical analysis (gauss or poisson distributions) you use the established methods of error calculation. If you have only a small number of results it´s without any sense to calculate average values or medians etc. So if you spent a little bit more information (possibly with an example) I could find a tip.
Like to add a remark. You can calculate errors not before you define a reference value. Thats what I´m missing most in your question.
You can calculate lim(deltaX/X) when X->0 using l'Hôpital's rule or graphically.
The relative error is important when X->0. E.g., detection limit.
Notice that deltaX does not satisfy all the hypotheses of the Hopital's rule. Moreover, the limit that is suggested does not exist.
I think the key is the value of references that you can use, for example I try to simulate a sum of forces acting on an object. In my study the summation of forces must be zero, but in the simulations obtain values of 0.01 [Nw]. The forces applied to the body are in the order of 200 [Nw]. As I consider both my relative error is on the order of 100% (0.01 [Nw] / 200 [Nw]) = 0.005%.
Try using the mixed error measure. Refer to the lecture notes by Istvan Maros on Computational Techniques for further details.
reading from wikipedia
https://en.wikipedia.org/wiki/Mean_absolute_percentage_error
They mention this problem. and they suggest two methods.
I tried one of them
https://en.wikipedia.org/wiki/Symmetric_Mean_Absolute_Percentage_Error
and it seems working. I got a good results with the third variant of the method.
ゼロ除算（division by zero）1/0=0、0/0=0、z/0=0
2018年05月28日(月) テーマ：数学
これは最も簡単な 典型的なゼロ除算の結果と言えます。 ユークリッド以来の驚嘆する、誰にも分る結果では ないでしょうか？
Hiroshi O. Is It Really Impossible To Divide By Zero?. Biostat Biometrics Open Acc J. 2018; 7(1): 555703. DOI: 10.19080/BBOJ.2018.07.555703
ゼロで分裂するのは本当に不可能ですか？ - Juniper Publishers
https://juniperpublishers.com/bboaj/pdf/BBOAJ.MS.ID.555703.pdf
再生核研究所 ゼロ除算の発見と重要性を指摘した：2014年2月2日
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