Re: Was there "legal" solution when the matrix is singular after GaussianElimination?



On Sat, 21 Apr 2007, dillogimp@xxxxxxxxx wrote:

hi

Was there "legal" solution when the matrix is singular after
GaussianElimination? That is, there are division by zero operations.

I suspect there is still "legal" solution but how to find those?
I have very good reason to suspect this, because I encounter singular
matrix, aka division by zero, but the problem should have solution.

As soon as there is "division by zero operations" the usual gaussian
elimination is "screwed" sorta speak. I bet people has encounter this
type pf problems very often. Please share your insight. Thanks.

First: Do some search on

Least Squares Method,
Moore-Penrose Pseudoinverse,
QR-factorization,
Singular Value Decomposition.

These tools are well-devepoled and tested for singular (and near-singular)
linear problems. If they help you, you do not need to read any further of
my response.

Can you specify some properties which may help?

How big is your matrix?

Is the matrix given exactly (such as, a matrix with integer, or rational
and exactly stored, entries)?

Or, are the entries given by approximate numbers (obtained from
measurements or so)?

In that case, was the "division by zero" actually "division by near-zero"
(resulting in overflow, or near-overflow)?

What version of Gauss elimination was used? Partial pivoting, complete
pivoting, or no-pivoting (relying on presumed (semi)definiteness or other
usable assumption)? (This happens with statistical calculations.)

During elimination, was the information about row operations recorded or
forgotten?

Is there a physical problem behind your system that has known
"conservation laws" or "solvability conditions"?

Or still something that I did not list?

Cheers, ZVK(Slavek).
.

Relevant Pages
Loading