Can one prove the accuracy of a solve routine when solving a set of 3-quadratic equations? Is there another strategy available for my problem (see text below) which does yield a sufficiently accurate (less than 0.1%) solution?

LS,

My name is Eric Kappel (Mathworks-ID: [e-mail]) with Matlab license listed below >> ver ----------------------------------------------------------------------------------------------------- MATLAB Version: 9.3.0.713579 (R2017b) MATLAB License Number: 40493049 Operating System: Mac OS X Version: 10.11.6 Build: 15G17023 Java Version: Java 1.8.0_121-b13 with Oracle Corporation Java HotSpot™ 64-Bit Server VM mixed mode -----------------------------------------------------------------------------------------------------

In the m-file “ellips_eq_poor_fit.m” in Archive.zip attachment I have used the “solve” routine to solve a set of 3 quadratic equations with 3 unknown parameters. The solution however has a poor-fit with the original data. (Use the publish-functionality in Matlab to see the background information and approach in the m-file.

In order to test the approach I tried the same approach in “ellips_eq_good_fit.m” using a 3 points from a known elliptical equation with the points chosen more separate than the original attempt. This trial yielded a good fit, telling me that the the original points are perhaps too close to each other to yield an accurate estimate. Hence the questions.

I hope you can help me with this problem, Kind regards,

Eric Kappel