Hi omorr, this is a useful reference for Andrey and plugin developers.
Could you elaborate more each section ? by specifying which features should be added/improved/corrected.

I updated the plugin now works more stable.

20 points (~24 sec). I made some little changes in Draghilev() function.

Yes, but initial value for a is X0 := stack(1, 1, 1, 1)

Edited by user 06 October 2012 18:22:31(UTC)  | Reason: Not specified

Please look at these matlab algorithms:

See pdfpage 112/docpage 90 of this document for a jacobian approximation by finite difference
http://www.dsic.upv.es/d...92/TesisEnriqueArias.pdf

Adaptive Robust Numerical Differentiation (matlab code)
http://www.mathworks.com...umerical-differentiation

Hello uni,

It seems very promising

As it is basically a linear regression over parameters (polynomial equation) I just added the result of it - just for checking. The results are very close to each other. It is interesting that the method is working on this problem very well
The determinant det((transpose(XX)*XX))=2.40082615642816*10^16is rather far from zero - well conditioned system. I suppose that would be very interesting to see what will happen when this determinant is quite close to zero - ill conditioned system. I suppose that the results must be quite different.

Regards,
Radovan

Hello kilele,

Thank you for the links. Actually, that is the point. At the moment, many plugins which rely on symbolic derivative, gradient, Jacobian, Hessian have great chance to fail sometimes due to the SMath symbolic restrictions and features or simply due to a complicated expressions obtained. There were many situations when you can actually have the numerical values of a vector valued function, but you can not have the derivatives of its elements (therefore, can not calculate Jacobian, Hessian etd.) and every method who use this will also fail (take a look for instance at the efforts of w3b5urf3r an the Nonlinear-solvers plugin). We can actually make Jacobian function ourselves (like the one very simple and hardly useful as in the attached example), but I think that is not the point. Numerical derivation methods are quite prone to errors and I would very like that someone make a plugin (based on some more sophisticated algorithms) like the one mentioned in your second link.

Regards,
Radovan

Edited by user 07 October 2012 14:31:21(UTC)  | Reason: Not specified

Do not worry about it uni ,

I think it is good enough that you solved many other examples including this particular problem .

Regards,
Radovan

Edited by user 08 October 2012 15:03:52(UTC)  | Reason: Not specified

Example 2. Finding roots: System 1 (Mathcad 15)

sys(x^2-y*x+y^2-1=0;sin(5*x^2)+sin(4*y^2)=0;2;1)

Edited by user 09 October 2012 09:52:27(UTC)  | Reason: Not specified

x1^3+x2^3-0.1e-1*sin(1.0001*x1+x2)=0;
One equation with two unknowns or implicitly given function. In the figure we can see the points at which violated the conditions of existence of an implicit function.

Draghilev's method.
x1 and x2 are solutions of this equation and are functions of the arc length, which allows a clear move along places where there are no implicit function in the classically accepted terms …