Wrote

I also agree about the mentioned observation on the 20-page of your reference. This is up to the user. A simple advice is to rearrange the function f(x)= 0 by avoiding division of terms when denominator can be close to zero.

Wrote

...about eval(), you cannot use it where there are undefined variables because the function "force" the numeric evalutation.

Wrote

Hello w3b5urf3r

Wrote

...about eval(), you cannot use it where there are undefined variables because the function "force" the numeric evaluation.

I am trying to figure out this regarding eval(). I do not get it. It is quite not logical to me. For instance, we can make a function in this way

[MATH=eng]f(x):line(a:x,y:eval(a^2+5*a-3),2,1)[/MATH]

We can call it and get the result

[MATH=eng]f(-2)=-9[/MATH] [MATH=eng]f(2)=11[/MATH]

But can not use it here

[MATH=eng]Bisection(f(x#),-9,0,10^{-5},50)=#@#[/MATH]

If we remove eval(), everything is fine

[MATH=eng]f(x):line(a:x,y:a^2+5*a-3,2,1)[/MATH]

[MATH=eng]Bisection(f(x#),-9,0,10^{-5},50)=-5.5414[/MATH]

There are functions like Bisection() that actually need the function value regardless the expression behind that function. Moreover, eval() has proven to be sometimes very useful in order to increase the calculation speed dramatically. I think this would be quite a restriction if we could not use it in the situation like these. I suppose that is due to the SMath design and its symbolic engine. I think this is quite a disadvantage regarding the strictly numerical computations and just hope that something could be done about it.

Regards,
Radovan

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hey w3b5urf3e, I see on the pic that you want to implement Brent, what about the BDQRF method mentioned on your Bisection testings file? they state that BDQRF is better than Brent

Wrote

I would not mind some derivation free optimization (minimization) functions in the plugin like BFGS or Nelder-Mead :d .

Wrote

Wrote

I would not mind some derivation free optimization (minimization) functions in the plugin like BFGS or Nelder-Mead :d .

There you have more matlab code by Kelley for Nelder-Mead and BFGS
( see bfgswopt.m ; nelder.m ; simpgrad.m )

As for "homotopy continuation methods" I've found this mathematica code.
However I don't know if this method is interesting or too difficult to code, I read that works very well for polynomial systems as well.

Wrote

Plugin updated.

Added the Newton-Raphson method for Nonlinear systems of equations and the Bisected Direct Quadratic Regula Falsi method.

regards,

w3b5urf3r

Wrote

Hello w3b5urf3r,

Do not have anything to say, but keep up this way

I hope you would not mind if I suggest you to change your convergence criterion in the root finding functions.
The convergence criterion at the moment is that the absolute function value in some iteration to be smaller than epsilon

[MATH=eng]abs(f(P3))
This is the simplest convergence criterion. Sometimes it is not good enough. To make that stronger you could add, for instance, that the absolute relative difference of two iteration be smaller than epsilon as well.

[MATH=eng](abs(f(P3))
The epsilon in the denominator is in the case the solution is zero.

Regards,
Radovan

Wrote

the second link is broken (mathematica code). Could you check it out.

Wrote

I know, but I'm trying to pay attention to the management of functions with unit of measurement... although I have not advertised this behavior, actually all solvers shown below works also with units. Introducing new covengence criteria preserving this aspect implies a more advanced error handling (and developping time)...

Wrote

Wrote

As for "homotopy continuation methods" I've found this mathematica code.
However I don't know if this method is interesting or too difficult to code, I read that works very well for polynomial systems as well.

EDIT:

More fortran and pseudocode about continuation methods on this pdf

little experiments in SMath with Homotopy... it's a very interesting and powerful tool b)


regards,

w3b5urf3r

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