Re: LU decomposition: backsubstitution available?

[John W. Eaton]

On 25-Mar-1998, Michael Hanke <address@hidden> wrote:

| In a matlab paper, I found a better solution as a side remark for
| sparse matrices: The matrix division routine checks before trying any
| LU decomposition if the matrix to be "inverted" is triangular (or a
| permuted triangular matrix). If so,
| the simple forward/backward substitution takes place. The amount for
| checking this property for full matrices is O(n^2). Maybe it is a
| better idea to carry a tag for every matrix??

Ugh.  Not very OO.  :-)

A better solution, and one that I would much prefer, would be to
convert the representation to be a triangular matrix object.

I have some plans to do this, but I'm not sure exactly how it will
happen.  One possibility is to convert Octave to use Blitz++ for
handling arrays and matrices (see http://monet.uwaterloo.ca/blitz/ for
more information about Blitz++).  I can see lots of reasons to do use
Blitz++, including the ability to handle special matrix classes
(including multidimensional matrices) relatively easily.  But there
are also some significant problems.  Blitz++ relies heavily on C++
templates, and gcc (even 2.8.1 and egcs) still seems to have trouble
with some of the Blitz++ code.  Also, Blitz++ is still in relatively
early stages of development, and so may not really be ready for some
time.

jwe