Finding all solutions to non-linear system numericaly

  • Thread starter Thread starter charnley
  • Start date Start date
  • Tags Tags
    Non-linear System
charnley
Messages
2
Reaction score
0
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?
 
Mathematics news on Phys.org
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?
 
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?
 
charnley said:
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.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

A How to use the Newton-Raphson method while keeping the sum constant?
Replies
2
Views
2K
B A symmetric problem has an asymmetric solution - why?
Replies
21
Views
2K
I Newton-Raphson Method With Complex Numbers
Replies
7
Views
2K
B System of linear equations: When are we guaranteed a unique solution?
Replies
5
Views
2K
B Can Linear Systems of Equations Have More Than Three Solutions?
Replies
29
Views
3K
I Different norms and how L1 leads to the sparsest solution
Replies
1
Views
1K
I Can Non-Linear Functions Be Converted to Linear Systems?
Replies
10
Views
2K
I How do you solve systems of equations in complex physics problems?
Replies
6
Views
2K
I Make Intelligent Initial Guesses for Newton-Raphson Programmatically
Replies
16
Views
3K
I Partial Differential Equation solved using Products
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top