Stability of the block cyclic reduction

AbstractThe forward stability of the block cyclic reduction without back substitution for block tridiagonal systems is studied. The basic assumption is that the matrix of the system is block column diagonally dominant. Then it is shown that for nonstrictly diagonally dominant matrices the forward error is O(Cnn2log2 nκϱ0), and for strictly diagonally dominant matrices it is O(Cng(s) log2 nκϱ0), where n is the block size of the matrix, N is the size of each block, g(s) is a function which measures the diagonal dominance, κ is a condition number, and ϱ0 is the machine roundoff unit. At the end some numerical evidence is presented