Block Tridiagonal Solver

Solves the block tridiagonal system Ax=d, where a, b, and c are the three diagonals of A.

% Solves the block tridiagonal system Ax=d, where a, b, and c are the three

% diagonals of A. If the size of the block is n-by-n, then b is M*n-by-n, d

% is M*n-by-*, a and c are each (M-1)*n-by-n.

%

% M = 12; n = 3;

% a = rand((M-1)*n,n); b = 3+2*rand(M*n,n); c = rand((M-1)*n,n);

% d = rand(M*n,10);

% x = BlockTriSolve(a, b, c, d);

%

% We can make block matrix A = BlockDiag(a, n, n, -1) + BlockDiag(b, n, n)

% + BlockDiag(c, n, n, 1); and then x = A\d to confirm the solution.

%

% Computational Cost of this method is 2M(13n^3/3+4n^2-4n/3). The cost is

% of order M*n^3. This is better than the backslash which is order (M*n)^3