> I understand the least squares in an overdetermined system. How is a least
> squares solution defined for an underdetermined system ?
> Any solution will satisfy AX-B = 0.
Perhaps the X with least squares norm is chosen? This is usually done
in linear least squares when the design matrix does not have full rank.
Reply by NewLine●January 20, 20062006-01-20
>> Hi,
>>
>> I was wondering if for an underdetermined system the Matlab mldivide
>> (equivalent to \) function will retrurn the minimum norm solution, or if
>> the
>> returned solution is constrained in another way or if the solution has no
>> particular properties beyond satisfying the set of equations ?
>>
>> The matlab help page doesn't help me.
>>
>> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
>
>>From the above link:
>
> "If A is an m-by-n matrix with m ~= n and B is a column vector with m
> components, or a matrix with several such columns, then X = A\B is the
> solution in the least squares sense to the under- or overdetermined
> system of equations AX = B."
>
I understand the least squares in an overdetermined system. How is a least
squares solution defined for an underdetermined system ?
Any solution will satisfy AX-B = 0.
Reply by Andor●January 20, 20062006-01-20
NewLine wrote:
> Hi,
>
> I was wondering if for an underdetermined system the Matlab mldivide
> (equivalent to \) function will retrurn the minimum norm solution, or if the
> returned solution is constrained in another way or if the solution has no
> particular properties beyond satisfying the set of equations ?
>
> The matlab help page doesn't help me.
>
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
>From the above link:
"If A is an m-by-n matrix with m ~= n and B is a column vector with m
components, or a matrix with several such columns, then X = A\B is the
solution in the least squares sense to the under- or overdetermined
system of equations AX = B."
Reply by Mike Yarwood●January 19, 20062006-01-19
"NewLine" <umts_remove_all_this@skynet.be> wrote in message
news:43cffb7d$0$4768$ba620e4c@news.skynet.be...
> Hi,
>
> I was wondering if for an underdetermined system the Matlab mldivide
> (equivalent to \) function will retrurn the minimum norm solution, or if
> the returned solution is constrained in another way or if the solution has
> no particular properties beyond satisfying the set of equations ?
>
> The matlab help page doesn't help me.
>
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
>
Hi,
I was wondering if for an underdetermined system the Matlab mldivide
(equivalent to \) function will retrurn the minimum norm solution, or if the
returned solution is constrained in another way or if the solution has no
particular properties beyond satisfying the set of equations ?
The matlab help page doesn't help me.
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
Thanks,
NL