Re: Question about LU decomposition

[Carlo de Falco]

On 19 Apr 2010, at 15:31, forkandwait wrote:

> Hi all,
>
> Let A = [2 4; 4 11].
>
> Then the output from the lu command is
>
> L = [1 0; 1/2 1]
> U = [4 11; 0 -3/2]
> P = [0 1; 1 0]
>
> This is great... but it is different from what would be generated if  
> the
> permutation hadn't been done first, which would have been
>
> L = [1 0; 2 1]
> U = [2 4; 0 3]
>
> This difference wouldn't be a problem, except I am just starting to  
> work
> through Gilbert Strang's "Intro to Applied Mathematics" using the  
> computer as a
> crutch (^H^H learning tool), and Octave's answers don't match the book
> (generally because he doesn't permute the matrices).  (This matrix  
> is on p 20).
>
> I am not sure what my question is exactly, but maybe for starts:
>
> (1) is there a way to run lu() without permuting?
yes but it is a dirty hack and is  only (questionably) useful if you  
want to check theoretical results:

[l, u] = lu(sparse(A), 0);
full(l)
full(u)
full(l*u-A)

> (2) what is the long story on permuting and LU decomposition -- is  
> it wrong to
> not permute?  Is there a relationship between all the possible  
> decompositions?
> etc etc (a link would be awesome...)
in general it is always a good idea to use pivoting (i.e. "permuting")  
to improve the numerical stability
of the algorithm, and it has an almost negligible cost, so avoiding  
pivoting never makes sense in numerics.

> Thanks again


HTH,
c.