How are you currently doing the computation?
Are the items on your diagonals symbolic or numeric?
It looks like your system might be block diagonal with a width of 3,except two of those put together? If so I am thinking that if you create a new matrix by folding the halves over, that might get you a true block diagonal, possibly width 6? There are techniques to work with block diagonals (though uniform width diagonals might be more efficient)
