>> load hwk7
>> who

Your variables are:

G         g         

>> p = colmmd(G);
>> [L,U] = lu(G(:,p));
>> nnz(L)+nnz(U),

ans =

        7697

>> p = symmmd(G);
>> [L,U] = lu(G(p,p));
>> nnz(L)+nnz(U),

ans =

       12013

>> p = symrcm(G);
>> [L,U] = lu(G(p,p));
>> nnz(L)+nnz(U),

ans =

       11451

>> p = colperm(G);
>> [L,U] = lu(G(:,p));
>> nnz(L)+nnz(U),

ans =

        4986

>> % this appears to be best
>> x = U\(L\g);
>> x(p) = x;
>> norm(G*x-g)

ans =

   9.5397e-14

>> % to do even better
>> [p,q,r,s] = dmperm(G);
>> r,s

r =

     1    21    41    51    61    81    91   111   121


s =

     1    21    41    51    61    81    91   111   121

>> size(G)

ans =

   120   120

>> % find out how much fill in generated in the block factorization
>> H = G(p,q);
>> totnnz = 0;
>> for i=1:8
Hi = H(r(i):r(i+1)-1,s(i):s(i+1)-1);
pi = colmmd(Hi);
[li,ui] = lu(Hi(:,pi));
totnnz = totnnz + nnz(li) + nnz(ui) - nnz(Hi);
end
>> totnnz+nnz(G)

ans =

        4410

>> % this has even smaller fill-in than colperm, so should use it
>> % however, too lazy to show how to do block back substitution.