Solve Nonlinear System of Equations

In summary, the speaker is seeking help with solving a system of nonlinear equations involving a set of vectors. They have attempted to use scipy.fsolve but have not been successful due to a mismatch in the number of inputs and outputs. They are looking for ways to over-constrain the problem or if they are missing something. The equations involve a set of 3x1 vectors and can be reduced to 12 equations, but they are not independent. They are asking for assistance or a routine in Matlab/Scipy.
  • #1
phil0stine
5
0
Hi, I have a set of vectors that I would like to solve for in a nonlinear system of equations.

I have tried to use scipy.fsolve to solve the system, but without success. I believe the problem is that scipy expects the same number of inputs as outputs. I have a 12x1 input vector, but I can only generate 9 independent equations.

I would appreciate any help with this, for example how I could over-constrain the problem, or am I missing something?

The vectors {C,R1,R2,R3} are all (3x1). There are also a set of (3x1) vectors {S1,S2,S3} that are known.

The equations are as follows:

CTR1=S1 (1)

CTR2=S2 (2)

CTR3=S3 (3)

and finally

[R1 R2 R3]T[R1 R2 R3]=I

which can be reduced to

R1TR1=R2TR2=R3TR3=1 (4,5,6)

R1TR2=R2TR3=R3TR1=0 (7,8,9)

R2TR1=R3TR2=R1TR3=0 Would give me 12 equations, but they are exactly the same as Equations 7,8,9.

So I don't know how to proceed. I would appreciate if anybody could point me in a direction, or to a matlab/scipy routine.
 
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  • #2
I think I have it, I cannot solve the system without an additional set of constraints.
 

What is a nonlinear system of equations?

A nonlinear system of equations is a set of equations that cannot be solved using basic algebraic methods. This is because the equations contain variables that are raised to powers or multiplied together, making it difficult to isolate a single variable.

How can I solve a nonlinear system of equations?

There are several methods for solving a nonlinear system of equations, including substitution, elimination, and graphical methods. You can also use numerical methods, such as Newton's method, to find approximate solutions.

Why is it important to solve a nonlinear system of equations?

Nonlinear systems of equations arise in many fields of science and engineering, including physics, biology, and economics. By solving these equations, we can better understand and model real-world situations, making it an important tool for scientists.

What are some challenges in solving nonlinear systems of equations?

One of the main challenges is that there is no one-size-fits-all method for solving these equations. The choice of method depends on the specific equations and variables involved. Additionally, some nonlinear systems may have multiple solutions or no solutions at all.

Are there any software or tools available to help solve nonlinear systems of equations?

Yes, there are various software programs and online tools that can assist with solving nonlinear systems of equations. These include graphing calculators, mathematical software programs, and online equation solvers. However, it is still important to understand the underlying concepts and methods for solving these equations.

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