Stability of block LULU factorization for block tridiagonal block HH-matrices

By a block representation of LULU factorization for a general matrix introduced by Amodio and Mazzia [P. Amodio, F. Mazzia, A new approach to the backward error analysis in the LULU factorization algorithm, BIT 39 (1999) 385–402], a block representation of block LULU factorization for block tridiagonal block HH-matrices is obtained and some properties on the factors of the factorization are presented. Perturbation theory for the block LULU factorization of block tridiagonal block HH-matrices is also considered. Then a rounding error analysis of the block LULU factorization for block tridiagonal block HH-matrices is given, and some bounds for the growth factor are proposed. Finally, a numerical example is presented to illustrate our theoretical results.