This paper develops algebraic and convergence properties of the left and right block reflectors used in the block diagonalization algorithm. Several numerical illustrations are reported.
Robbe, M., & Sadkane, M. (2005). Convergence analysis of the block Householder block diagonalization algorithm. Bit (Lisse) : numerical mathematics, 45(1), 181-195. https://doi.org/10.1007/s10543-005-2648-6 (Original work published 2005)