Create banded matrix from arbitrary real square matrix

Create a banded matrix B with bandwidth bw from an arbitrary real square matrix A

Create a banded matrix B with bandwidth bw from an arbitrary real square matrix A using a similarity transformation.

[B, T, Ti] = banddiag(A, bw) produces a banded matrix B with bandwidth bw and the similarity transformation matrix T and its inverse Ti so that B = T*A*Ti and T*Ti = I. The matrix B has nonzero entries only on the main diagonal and bw diagonals on either side.

The Algorithm uses successive QR steps to reduce the input matrix A to a banddiagonal structure.

The bandwidth bw is an integer with bw > 0. For b == 1, the matrix B becomes tridiagonal and for bw >= n-1, the matrix B is equal to A.