Newton method

#1 Pubblicato: 08/04/2023 16:07:23

67 apprezzamenti in 713 post.

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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) scaricato 993 volta(e).

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Martin Kraska 09/04/2023 08:50:00

#2 Pubblicato: 09/04/2023 08:56:19

Martin Kraska

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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) scaricato 1564 volta(e).

And this is the modified version.

Newton2Da.sm (19,03 KiB) scaricato 1688 volta(e).

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

#3 Pubblicato: 09/04/2023 14:27:18

Jean Giraud

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Wrote
... can't find 2nd root

2nd root confirmed exact.

Solve(f,q,x0,x1,TOL) Copy.sm (162,62 KiB) scaricato 1685 volta(e).

#4 Pubblicato: 09/04/2023 14:33:35

overlord

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Tried to solve your functions with al_nleqsolve().

Regards

Newton.sm (13,85 KiB) scaricato 1603 volta(e).

#5 Pubblicato: 09/04/2023 18:19:38

Alvaro

1.139 apprezzamenti in 1.805 post.

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

Newton2Da.sm (13,34 KiB) scaricato 1732 volta(e).

Best regards.
Alvaro.

#6 Pubblicato: 10/04/2023 12:25:58

Jean Giraud

983 apprezzamenti in 6.866 post.

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

#7 Pubblicato: 10/04/2023 16:21:38

overlord

600 apprezzamenti in 1.381 post.

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Wrote
I cannot use the roots function

Actually, you can.

Regards

#8 Pubblicato: 10/04/2023 20:29:31

Jean Giraud

983 apprezzamenti in 6.866 post.

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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) scaricato 1676 volta(e).

#9 Pubblicato: 11/04/2023 14:21:16

Alvaro

1.139 apprezzamenti in 1.805 post.

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Two variations added.

Newton2Da. v2.sm (38,35 KiB) scaricato 1676 volta(e).

Newton2Da. v2.pdf (152,11 KiB) scaricato 1148 volta(e).

Best regards.
Alvaro.

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sergio 03/05/2023 14:29:00

#10 Pubblicato: 03/05/2023 00:37:31

Valery Ochkov

67 apprezzamenti in 713 post.

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Wrote
Two variations added.

Newton2Da. v2.sm (38,35 KiB) scaricato 1676 volta(e).

Newton2Da. v2.pdf (152,11 KiB) scaricato 1148 volta(e).

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!

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Alvaro 03/05/2023 03:21:00

#11 Pubblicato: 03/05/2023 12:02:25

Jean Giraud

983 apprezzamenti in 6.866 post.

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You may find this Treasury useful/productive.

Solve(f,q,x0,x1,TOL) Copy.sm (300,16 KiB) scaricato 1708 volta(e).

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Newton method - Messaggi