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I'm trying to solve a system of 5+ equations for 3 unknowns, preferably using the least-squares method. I've Solve will not return solutions for more equations than you have unknowns. Fit does not work because my equations have 4 sets of data.
Si=a*Ui + b*Vi + c*Wi, where i goes from 1 to 5
U, V, and W all come from a table, and S is from experimental data.
I need to know how to solve for a,b,c given more than 3 equations.
Background: The problem is actually trying to solve for Judd-Ofelt parameters of a laser crystal. S is the experimental line strength and U, V, and W are the doubly reduced unit-tensor operators for the corresponding line. a, b, c is the Omega2, Omega4, and Omega6 Judd-Ofelt parameters. There can be 20 or more lines, or 20 or more equations to limit/solve for a,b,c.