Finding all solutions to non-linear system numericaly

[charnley]

Hello world,

Is it possible to find all solutions to a system of non-linear equations, without solving them analytically?

I have implemented a python solution of Newton's Method, is there a method of getting good guesses without scanning all numbers?

 

[HallsofIvy]

What do you mean by "find all solutions"? You can, of course, approximate solutions. Is that what you mean by "finding" them? All numerical methods of solving equations will give one equation- typically, though not necessarily, the one closest to the chosen "starting value". So to find "all" solutions you would have to have some information about their possible values to begin with. And how would you know if you had found all solutions? What about equations that have an infinite number of solutions?

 

[charnley]

By "find all solutions" I mean finding the roots. Is there a way to, numerically, analyse the functions. If I *don't* have any information about their possible values to begin with, find all possible roots.

Hmm, I actually did no consider a system with infinite number of solutions. Hmm.

So there is no way to find all roots, without doing a analytical analysis of the system?

 

[AlephZero]

So there is no way to find all roots, without doing a analytical analysis of the system?

Correct. If you don't do some analysis, you don't even know how many roots there are.