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.