
Solving N1 equations in N unknowns with initial state?
Posted:
May 7, 2013 11:56 AM


I have a system of N1 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 nonrecursive method from the equations and the initial values?

