Skip to main content
3-Newcomer
January 22, 2025
Solved

Non- linear equations system solution Gradient descent

  • January 22, 2025
  • 2 replies
  • 1759 views

Hello everyone, maybe someone can help me solve or has a ready-made solution for solving a system of nonlinear equations by the gradient descent method. I use PTC Mathcad Express Prime 9.0.0.0

_12762755_0-1737536391415.png

 

Best answer by LucMeekes

Incorrect, check the results. You have a square z in the first row, instead of just z.

LucMeekes_0-1737545566490.png

LucMeekes_1-1737545632140.png

There are two possible solutions, one is: 1, 1, 3/10 (exactly).

Proof:

LucMeekes_2-1737545712162.png

 

The other is approximately

LucMeekes_4-1737546049664.png

 

Success!
Luc

 

2 replies

21-Topaz II
January 22, 2025

This is one solution but is possibly not the only one.

Capture.JPG

3-Newcomer
January 22, 2025

Thanks can you send a file?

19-Tanzanite
January 22, 2025

As Cornel noted, there are 8 solutions.  The attached shows how to find them in an Express version of Prime, where there are no solve blocks available.

Just set the value of "column" to any integer between 0 and 7 inclusive to find the various solutions.  (I used Prime 8 Express, so you should be able to load it directly into Prime 9 Express).

 

Alan

23-Emerald IV
January 22, 2025

Thanks Alan for this nice algorithm.

I've created a function Solve for it that (of course) works in Prime Express:

LucMeekes_0-1737582724304.png

Enjoy!
Luc

 

19-Tanzanite
January 23, 2025

Very clever solve function definition Luc, well done!

 

Alan