http://www.mapleprimes.com/questions/143540-How-To-Interpolate-Roots-For-A-Curve en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 03:13:18 GMT Thu, 11 Jun 2026 03:13:18 GMT The latest answers and comments added to the Question, How to interpolate roots for a curve expressed in numerical arrays http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/143540-How-To-Interpolate-Roots-For-A-Curve http://www.mapleprimes.com/questions/143540-How-To-Interpolate-Roots-For-A-Curve?ref=Feed:MaplePrimes:How to interpolate roots for a curve expressed in numerical arrays:Comments#answer143543 <p>Quite often a good way to do this is to set it up with dsolve/numeric's <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=dsolve/numeric/Events">events</a> functionality. The solver itself is in charge of tracking its own tolerances internally, and adjusting stepping dynamically, and letting it do that with the goal of noticing a particular event (such as hitting a zero) makes a lot of sense. Slightly less good (sometimes, b/c the accuracy of the procs emitted by dsolve/numeric are only as good as the piecewise polynomial interpolants that get set up) is to do rootfinding (fsolve, DirectSearch, etc) on option listprocedure output. And interpolating an array of data points (output from dsolve/numeric at steps chosen by the programmer) can be worse, since that data can lack any finer grained stepping that dsolve/numerics solver might have had to do near a root.</p> <!--break--> <p>By the way, you should be able to find several older posts that relate; just use the search field at the top of this site's pages. (eg. searching for <em>events</em> gets&nbsp;<a href="http://www.mapleprimes.com/questions/125273-Dsolve-Events-How-To-Control-For-A-Sign-Change">here</a>, <a href="http://www.mapleprimes.com/questions/37819-The-Mysterious-events-Command">here</a>, etc.)</p> <p>acer</p> <p>Quite often a good way to do this is to set it up with dsolve/numeric's <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=dsolve/numeric/Events">events</a> functionality. The solver itself is in charge of tracking its own tolerances internally, and adjusting stepping dynamically, and letting it do that with the goal of noticing a particular event (such as hitting a zero) makes a lot of sense. Slightly less good (sometimes, b/c the accuracy of the procs emitted by dsolve/numeric are only as good as the piecewise polynomial interpolants that get set up) is to do rootfinding (fsolve, DirectSearch, etc) on option listprocedure output. And interpolating an array of data points (output from dsolve/numeric at steps chosen by the programmer) can be worse, since that data can lack any finer grained stepping that dsolve/numerics solver might have had to do near a root.</p> <!--break--> <p>By the way, you should be able to find several older posts that relate; just use the search field at the top of this site's pages. (eg. searching for <em>events</em> gets&nbsp;<a href="http://www.mapleprimes.com/questions/125273-Dsolve-Events-How-To-Control-For-A-Sign-Change">here</a>, <a href="http://www.mapleprimes.com/questions/37819-The-Mysterious-events-Command">here</a>, etc.)</p> <p>acer</p> 143543 Sat, 16 Feb 2013 02:58:11 Z acer acer http://www.mapleprimes.com/questions/143540-How-To-Interpolate-Roots-For-A-Curve?ref=Feed:MaplePrimes:How to interpolate roots for a curve expressed in numerical arrays:Comments#comment143546 <p>Thank you! This is very helpful, I think an event with a halt would do it nicely.</p> <p>Thank you! This is very helpful, I think an event with a halt would do it nicely.</p> 143546 Sat, 16 Feb 2013 08:43:07 Z mapleq2013 mapleq2013