Re: How to solve the system of linear equations?

• To: mathgroup at smc.vnet.net
• Subject: [mg25450] Re: How to solve the system of linear equations?
• From: Jeff DuMonthier <jeff at lheapop.gsfc.nasa.gov>
• Date: Sun, 1 Oct 2000 02:44:31 -0400 (EDT)
• Organization: NASA Goddard Space Flight Center (skates.gsfc.nasa.gov)
• References: <8r17ui\$h8r@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <8r17ui\$h8r at smc.vnet.net>, Zak Levi <zaklevi at yahoo.com>
wrote:

> Dear Mathematica experts,
>
> How to solve, in Mathematica, the system of linear equations,
>
> when a number of equations is larger than a number of variables.
>
> Another system easily pass to apply LSM in this case, but it seems to
> me that there is no such opportunity in Mathematica.
>
> As an application, given N>5 points at plane, how to calculate (the
> parameters) of best fitting ellipse.
>
> Thanks a lot,
> ZL

This is what I have done before:

FindMinimum[Apply[Plus, Map[(# #)&,
{A11 X1 + A12 X2 + ... + A1n Xn - B1,
A21 X1 + A22 X2 + ... + A2n Xn - B2,
...
Am1 X1 + Am2 X2 + ... + Amn Xn - Bm} ] ],
{X1, 0.0}, {X2, 0.0}, ... {Xn, 0.0} ]

This is a least square error minimization for m equations in n
variables (m >= n) in the standard A X = B form. The (# #) is because I
can't do exponents in plain text.  You may have to change the zeros to
some other appropriate initial conditions.

```

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