Re: Question about LU decomposition

[James Sherman Jr.]

I don't have an intimate knowledge of the algorithm that Octave uses for LU decomposition, but I believe it is normal for problems like this to assume that permuting the rows doesn't change the nature of the problem (say solving the system Ax = b, since you can just permute the rows of b as well).  Its certainly not wrong to not permute, but its an side-effect of the algorithm that Octave uses to calculate the decomposition that improves performance.

But I mean, if you're just using to check the book, the solution is much easier than that.  Just see if the L/U matricies are lower/upper triangular and multiply them together to see if you get the matrix A.  If you're making up your own examples, then choose your A matrix, then run the lu function, then take the permutation from that, apply it to A, and then do your method by hand on the permuted matrix.

And on your second email, I don't have the book that you're referring to, but I imagine that the problem is that, while A is symmetric positive and definite, the permuted matrix (the matrix that the L and U are for) is not.

I don't have Octave available currently, but I believe there is an ldl function that you could use for doing the LDL factorization.

Hope this helps.

On Mon, Apr 19, 2010 at 10:47 AM, forkandwait <address@hidden> wrote:

>

Sorry to self reply, but ...

Octave's results for lu() Strang's LDL' factorization not work (right around
the pages mentioned below), which is basically A = L * diag(diag(U)) * L' for a
symmetric positive definite matrix.

Also, I am sure there is a ton of theory behind all this that I don't know; if
I did, I might think my questions naive...  A link would be awesome, but I
don't expect anyone to write up a lecture (though I would read it if they
did....)

Thanks again!


_______________________________________________
Help-octave mailing list
address@hidden
https://www-old.cae.wisc.edu/mailman/listinfo/help-octave