How to use parallel computing

I have a problem in solving computation of matrix of which form is Ax=b. It takes so long time over several hours. the form of each matrix is (B C 0 0 0 0 . . . B1 C1 0 0 0 0) (x1) (b1) (A B C 0 0 0 . . . A1 B1 C1 0 0 0) (x2) (b2) (0 A B C 0 0 . . . 0 A1 B1 C1 0 0) (x3) (b3) (. . . . . . . . . . . . . . . ..) (...) = (..) (0 0 0 A B C . . . 0 0 0 A1 B1 C1) (xN-1) (bN-1) (0 0 0 0 A B . . . 0 0 0 0 A1 B1) (xN) (bN) I want to use parallel computing for this in fast time. is there anybody who helps me work this and let me know?

[Walter Roberson]

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)