When I run the following (in Matlab) on a sparse matrix $A$, I get larger band width. The
symrcm (symmetric reverse Cuthill-McKee permutation) is not guarenteed to find the smallest band width, but it makes no sense for it to increase. What is wrong here?
reorderingForSmallBand = symrcm(A); A = A(reorderingForSmallBand,reorderingForSmallBand);
Originally, my matrix $A$ has this form (PDF). I also wonder if it is a big deal to have large bandwidth as the backslash solver in Matlab says it is above the limit for a solver exploiting the banded structure. Is it any advantage for an iterative solver to have small band width?