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Topic: conditon of a matrix
Replies: 4   Last Post: Mar 28, 2011 10:53 PM

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Kevin Hung

Posts: 81
Registered: 12/7/04
Re: conditon of a matrix
Posted: Mar 28, 2011 10:53 PM
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Hi Greg,

You are correct. In fact,

(1) pinv(K)*F will give the minimum norm solution

(2) K \ F will give the solution vector x that has the minimum number of nonzero elements.

I learned about these 2 solutions from Mr. Cleve Moler's article "The world smallest impossible problem". I think you can get it in Mathworks website. Very good article.

Kevin

Greg Heath <heath@alumni.brown.edu> wrote in message <5b712702-5957-440f-95a4-810f3660878e@h38g2000yqn.googlegroups.com>...
> On Mar 28, 11:23 am, "Kevin" <kh...@fake.com> wrote:
> > There is another option. If for whatever reason, you don't like the solution from "K\F", then try this
> >
> > pinv(K)*F.
> >
> > I believe this will give you a different answer for x but the residual error would still be small. In this case the vector x contains the minimum number of nonzero entries.

>
> On the contrary. In order to obtain the minimum norm
> solution, all elements must be nonzero.
>
> On the other hand, the backslash solution will tend to have
> the maximum number of zero elements.
>
> Hope this helps.
>
> Greg




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