You have to be aware that your task has an infinite number of soltions:
So you will have to resort to numerical methods and you have the choice amongst two.
The "root" command usually works pretty well and there are two ways of using it - provinding an interval or providing a guess value. Usually different guesses would give you different solutions, but in case of your equation we get the very same result most of the times - crazy.
Sorry - I have used Prime 3.1
And second!
Without the vectorization - no ansver
With the vectorization - crash! Check please
My Solutions are:
MP4
and with MC15 the same solution:
EDIT: MP4 with TOL=10^-7 and MC15 with TOL=0.001
MP4 with TOL=0.001 i got the same results.
I have no idea why the root function behaves so differently with different guess values.
But in mathcad 11, there is a way to show the steps that the root function takes. ( I guess it won't work in Mathcad 15, but please try).
Here's the function, and a couple of examples of its usage with the function: tan(x)-x-0.48:
In most cases root finds the positive value closest to zero, unless the guess valua is close to another solution.
This is also illustrated by a scan of guess values:
Note that the trace is absent at times, that's when a complex root was found.
Oh, and my TOL=10^-7.
Luc
You are right. RootPath does not work in MC15. The return vector would only contain the last guess (aka the solution).
Only ways I can think of to get the interim guess values of the algorithm is either to throw in a trace-command in the function and turn on debug mode. or throw in a READPRN command which appends the current argument to a data file.
Both ways would slow down calculations significantly.
I get the following in MC15:
I can't explain the difference between the implicit and explicit vectorisations!
TOL is the default 10^-3; however, setting it much tighter didn't alter anything.
Alan
Interesting effects we experience here.
Here is a nother one (done in MC15). I always thought that "root" would use the same LM algorithm as "Find" in the solve block (not in Prime as here we have the Knitro algorithms). Obviously root works in a different way, not sure how. Most of the times we get 0,966. Only with some selected guess values we get a different result.
The algorithm in the solve block for "Find" was set to "Levenberg-Marquardt" (default). "Conjugate Gradient" and "Quasi Newton" give the very same result with exception of guess value 0 - here "Conjugate Gradient" returns 0,966 and no errror.
