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.