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Topic: Solving N-1 equations in N unknowns with initial state?
Replies: 4   Last Post: May 9, 2013 1:23 PM

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 Don Del Grande Posts: 1 Registered: 5/7/13
Solving N-1 equations in N unknowns with initial state?
Posted: May 7, 2013 11:56 AM

I have a system of N-1 equations in N unknowns.

If I start by assigning values to the N unknowns and then recalculate the values recursively:

(a) Will they always reach a single solution (assuming there is a solution for the equations in the first place), and

(b) If a single solution can be reached, is there a way to determine it in terms of the initial values without having to go through the recursion, and if so, what is it?

Example:
3a - b - c - d = 9
-a + 3b - c - d = 3
-a - b + 3c - d = -3
-a - b - c + 3d = -9

If you combine the first three equations, you get a + b + c - 3d = 9, which is -1 times the fourth equation, so it is effectively 3 equations in 4 unknowns.

If the values are initially set to a = 3, b = 1, c = -1, and d = -3, and the equations repeated recalculated recursively, they eventually become a = 9/4, b = 3/4, c = -3/4, and d = -9/4.

Can those values be determined in a non-recursive method from the equations and the initial values?

Date Subject Author
5/7/13 Don Del Grande
5/7/13 Ken.Pledger@vuw.ac.nz
5/7/13 Don Del Grande
5/9/13 gnasher729
5/8/13 William Elliot