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I am wondering what my best approach is in the following scenario. I have 8 unknowns, however a virtually unlimited number of non-linear equations which makes the system over-determined.

unknowns:

U M V N J S W N

equations:

U*M + V * Catime1 – V*M – Mgtime1 = 0
J*M + W * Catime1 – W*M – Srtime1 = 0
U*N + V * Catime2 – V*N – Mgtime2 = 0
J*N + W * Catime2 – W*N – Srtime2 = 0
U*S + V * Catime3 – V*S - Mgtime3 = 0
J*S + W * Catime3 – W*S - Srtime3 = 0
U*T + V * Catime4 – W*S - Mgtime4 = 0
J*T + W * Catime4 – W*S - Srtime4 = 0

Here's what I need help with:

1) identify which Matlab (or even within python) function will solve this set of equations.

2) generate the input (equations) using python using a large Catime(i-1) and Srtime(i-1) data-set.

Shai
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raincity1199
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  • if the solution is not unique, are you looking for a formula of all possible solutions, or do you just want any one solution? Check out this summary page: http://www.mathworks.com/help/matlab/math/systems-of-linear-equations.html – Amro May 27 '13 at 23:49
  • @Amro - overdetermined, so unlikely an exact solution exists period, never mind uniqueness. –  May 28 '13 at 01:16
  • of course, what @woodchips said :) – Amro May 28 '13 at 17:21
  • I see now Ill get a least squares fit to the data. I am unsure though, after I define Catime, Mgtime, and Srtime (which is my experimental data), how I define the equations... – raincity1199 May 29 '13 at 04:04
  • There is no such thing as an unlimited number of constraints (virtually or otherwise) on a system. I believe that you have a fundamental misunderstanding of your problem. – Slater Victoroff Jul 02 '13 at 14:52

1 Answers1

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Write the problem as a Non Linear Least Squares problem and try to minimize it.

This will handle correctly the additional data you have.

Royi
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