? types of LS

Cheng Cosine · science forum Guru Wannabe Joined: 26 May 2005 Posts: 168

Hi:

So far I saw ordinary LS, recursive LS, weighted LS, and total LS.
Whatelse?

For weighted LS, we look for min( norm(err,W) ), where norm(err,W) =

sqrt( err'*W*err ). W is positive definite. The easiest W is a diagonal
square

matrix with positive diagonal entries, W = D. Since Forbinous norm is
untinarily

invariant, we can extend W = U*D*U', where U is square unitary matrix. But
will

this have any effect on the LS soln we found when different U's are used?

For total LS, the problem is defined as min( norm( [A, a]-[AEst, aEst] ),
Forbinous ) under

condition that [AEst, aEst] belongs to R^Mx(N+1) and subject to aEst belongs

to range(AEst). A is MxN, x is Nx1, a is Mx1, M > N. [A, a] is argumented
matrix

in MatLab notation. That is, we know A*x = a, but we only have AEst and aEst
and

want to find some best approximted soln to A*x = a. How to solve problem
like this?

What if M <= N, and wnat to find its best approximted soln?

Thanks,
by Cheng Cosine
Jul/18/2k6 NC

Han de Bruijn · science forum Guru Joined: 18 May 2005 Posts: 1285

Cheng Cosine wrote:

Cheng Cosine · science forum Guru Wannabe Joined: 26 May 2005 Posts: 168

"Han de Bruijn" <Han.deBruijn@DTO.TUDelft.NL> wrote in message
news:6708c$44bca4c1$82a1e228$5632@news1.tudelft.nl...

Peter Spellucci · science forum Guru Joined: 29 Apr 2005 Posts: 702

In article <7Dcvg.62598$R26.24864@tornado.southeast.rr.com>,
"Cheng Cosine" <acosine@spamfree.com> writes:

Google