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 (1.07 MiB) downloaded 599 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 (21.4 KiB) downloaded 1010 time(s).

And this is the modified version.


Newton2Da.sm (19.03 KiB) downloaded 1111 time(s).

Wrote

... can't find 2nd root

2nd root confirmed exact.

Solve(f,q,x0,x1,TOL) Copy.sm (162.62 KiB) downloaded 1070 time(s).

Tried to solve your functions with al_nleqsolve().

Regards

Newton.sm (13.85 KiB) downloaded 1055 time(s).

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

Newton2Da.sm (13.34 KiB) downloaded 1166 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 (27.42 KiB) downloaded 1107 time(s).

Two variations added.

Newton2Da. v2.sm (38.35 KiB) downloaded 1094 time(s).

Newton2Da. v2.pdf (152.11 KiB) downloaded 639 time(s).

Best regards.
Alvaro.

Wrote

Two variations added.

Newton2Da. v2.sm (38.35 KiB) downloaded 1094 time(s).

Newton2Da. v2.pdf (152.11 KiB) downloaded 639 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 (300.16 KiB) downloaded 1076 time(s).