Non- linear equations system solution Gradient descent

[GrigoriyUkraine]

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

[terryhendicott]

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

[GrigoriyUkraine]

Thanks can you send a file?

[LucMeekes · Accepted solution]

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

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

Proof:

The other is approximately

Success!
Luc

[Cornel]

I think there are in fact eight solutions (or at least eight)...:

[GrigoriyUkraine]

Thaks a lot 

[LucMeekes]

I guess you are right. The solution with x=-0.853 is one of a 7th order polynomial.

Luc

[AlanStevens]

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

[LucMeekes]

Thanks Alan for this nice algorithm.

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

Enjoy!
Luc

[AlanStevens]

Very clever solve function definition Luc, well done!

Alan