Stability of block LU factorization for block tridiagonal matrices

It is showed that if AA is I-block diagonally dominant (II-block diagonally dominant), then the reduced matrix SS preserves the same property. We also give a sufficient condition for the reduced matrix SS also to be a block HH-matrix when AA is a block HH-matrix, and some properties on the comparison matrices μI(A(k))μI(A(k)), μII(A(k))μII(A(k)), μI(L)μI(L), and μI(U)μI(U) are obtained. Finally, error analysis of block LU factorization for block tridiagonal matrix is presented.