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#### least squares fit

```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.

``` 0 3/6/2004 3:31:21 PM comp.soft-sys.matlab  211266 articles. 25 followers. 1 Replies 503 Views Similar Articles

[PageSpeed] 58

```<...hosam wants to solve a system of equations in Mathematica...I
guess...>

> Solve[]
> Fit[]
[snip]

wrong NG I guess. You've posted on

comp.soft-sys.matlab

Try

comp.soft-sys.math.mathematica

Anyway:
In Matlab: solve(),fzero(),fsolve(),etc
In Mathematica: Solve[], NSolve[], FindZero[], LinearSolve[]
``` 0 3/6/2004 4:00:28 PM