I cannot use the roots function and must use one old good simple method by Newton.
What can you say about it?

Newton-Eng.docx (1 MiB) downloaded 77 time(s).

Very nice.

I had problems when reproducing your 2D version. Depending on initial guess I got errors "requested matrix element does not exist". The situation seemed to improve a little by pre-allocating the vectors X and Y yet it didn't become really robust.

So instead of assigning to j+1 elements I used augment() to add new points to the iteration history.

This is the original version:


Newton2D.sm (21 KiB) downloaded 67 time(s).

And this is the modified version.


Newton2Da.sm (19 KiB) downloaded 61 time(s).

Wrote

... can't find 2nd root

2nd root confirmed exact.

Solve(f,q,x0,x1,TOL) Copy.sm (162 KiB) downloaded 53 time(s).

Tried to solve your functions with al_nleqsolve().

Regards

Newton.sm (13 KiB) downloaded 57 time(s).

Another way, keeping the mathematical formulation and the iteration algorithm separate. As here.

Newton2Da.sm (13 KiB) downloaded 61 time(s).



Best regards.
Alvaro.

Thanks Alvaro, added to my next Samples visit.
Take care ... Jean

Wrote

I cannot use the roots function

Actually, you can.

Regards

Wrote

I cannot use the roots function and must use one old good simple method by Newton.
What can you say about it?

An old vintage in Smath ... two examples.
Take care Valery ... Jean.

Solve_roost f1(x,y). f2(x,y).sm (27 KiB) downloaded 57 time(s).

Two variations added.

Newton2Da. v2.sm (38 KiB) downloaded 83 time(s).

Newton2Da. v2.pdf (152 KiB) downloaded 76 time(s).

Best regards.
Alvaro.

Wrote

Two variations added.

Newton2Da. v2.sm (38 KiB) downloaded 83 time(s).

Newton2Da. v2.pdf (152 KiB) downloaded 76 time(s).

Best regards.
Alvaro.

From my future article
Если уравнений не два, а три, то матрица Якоби будет состоять из трёх строк и трёх столбцов. При этом графически отображать решение придётся не двумя кривыми, а тремя поверхностями на 3D-графике, причём их взаимное пересечение и будет отмечать решение (задание читателю).
Слабо!

You may find this Treasury useful/productive.


Solve(f,q,x0,x1,TOL) Copy.sm (300 KiB) downloaded 64 time(s).