0
$\begingroup$

I was reading this paper http://www.ersavas.com/bulut/projects/algorithms/smo_ge.pdf where it deals with solving linear equations with sparse matrices

So lets say we have an equations

Ax=b where A is a sparse matrix, then we can solve it using Gaussian elimination.

but first we can order A so that is has lesser band itself. So lets say I have a matrix

A = a11  0    a13  0     0    a22  a23  a24     a31  a32  a33  0     0    a42  0    a44 

Then if I permute using $$ \pi=\{1, 2, 3, 4\} $$

The linear system after symmetric permutation will have

A = a11  a13  0    0     a31  a33  a32  0     0    a23  a22  a24     0    0    a42  a44 

but if we actually change matrix A to the above form using permutation is the equation

Ax=b still valid

Also the paper mentions about reverse Cuthill-McKee Ordering, and states that it is efficient in comparision to just Cuthill-McKee Ordering for Gaussian elimination because of the way it is performed (left to right and down to bottom).

I didn't get what it meant by (left to right and down to bottom). Any insights?

1 Answers 1