http://www.mapleprimes.com/maplesoftblog/137375-Further-Analysis-Of-A-Minimization-Problem en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 12:18:18 GMT Tue, 09 Jun 2026 12:18:18 GMT The latest comments added to the Blog Entry, Further Analysis of a Minimization Problem: Distance from a Point to a Curve http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/maplesoftblog/137375-Further-Analysis-Of-A-Minimization-Problem http://www.mapleprimes.com/maplesoftblog/137375-Further-Analysis-Of-A-Minimization-Problem?ref=Feed:MaplePrimes:Further Analysis of a Minimization Problem: Distance from a Point to a Curve:Comments#comment138884 <p>On re-reading this it occurred to me that this distance is also a useful quantity when trying to fit a function to a data set where the independent-variable values have errors.</p> <p>E.g. often I want to fit y=f([parameters],x) to a data set [[x],[y]] weighted with the errorbar on the values in [y]. If the values in [x] are exact it is easy: find the expressions for the rms deviation of y from f([parameters],x) (i.e. the penalty function) with proper weighting &amp; minimize that by varying parameters, with an appropriate method. Packages in Maple will do this for me. If the values in [x] also have errors, it is not so obvious how to do it right. I have read of heuristic schemes where df/dx at the values of [x] is used to estimate the increase in error bar in the values in [y] due to the uncertainty in x, but that is inaccurate for all but the most well-behaved functions f, and not shown to be correct--or even approximately so---in any rigorous sense.</p> <p>Using the distance of f(x) to the data points as penalty function seems like a much more rigorous---if more complex---way to do this. Now the errors in both x and y are easily incorporated in weighting the rms&nbsp; deviation (now: distance) of function to data. Interestingly enough; this example also exposes the difficulty of practical application: The distance of a data point to a curve (usually defined as the length of the shortest vector from the data point to a point on the curve that is normal to the tangent of the function at that point) is not in general a unique value making its evaluation a bit of a pain, even more so at higher dimensions.</p> <p>This is fun. Experts in this field probably know all this; but re-reading this post made me realise what is going on in such fitting problems (which I have occasionally had to deal with). So, thanks for this post.</p> <p>Mac Dude.</p> The latest comments added to the Blog Entry, Further Analysis of a Minimization Problem: Distance from a Point to a Curve 138884 Sat, 27 Oct 2012 16:09:09 Z Mac Dude Mac Dude http://www.mapleprimes.com/maplesoftblog/137375-Further-Analysis-Of-A-Minimization-Problem?ref=Feed:MaplePrimes:Further Analysis of a Minimization Problem: Distance from a Point to a Curve:Comments#comment202888 <p>How do you access the code for the animation?&nbsp; Thanks.</p> <p>&nbsp;</p> <p>Benzaid</p> The latest comments added to the Blog Entry, Further Analysis of a Minimization Problem: Distance from a Point to a Curve 202888 Tue, 12 Dec 2017 16:47:46 Z Benzaid Benzaid