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#1 2006-01-26 04:07:43

dimischka
Guest

Solving a system on nonlinear equations

Can we prove the existence of a unique solution of a square system of nonlinear equations? Where the number of equations equal the number of constraints and all equations are indepedent.

#2 2006-01-26 06:02:10

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Solving a system on nonlinear equations

Consider the square, nonlinear, independant equations:

x² + y² = 0
x² + y² = 1

In short, the answer is no.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-01-26 06:29:25

dimischka
Guest

Re: Solving a system on nonlinear equations

Thank you.

How about convergence to a solution, is that provable?

#4 2006-01-26 06:35:15

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Solving a system on nonlinear equations

Convergence of a solution?  Convergence is normally described for a function, not an equation.  I'm not sure what you mean by convergence in this context.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#5 2006-01-26 06:41:16

dimischka
Guest

Re: Solving a system on nonlinear equations

Sorry I'm not articulate enough.

What I meant is if I have a set of nolinear equations, how can I prove that there is indeed a solution to that system?

Thanks.

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