Block $LU$ factorization is stable for block matrices whose inverses are block diagonally dominant
A. George, Kh. D. Ikramov

References
1.	A. George, Kh. D. Ikramov, “Gaussian elimination is stable for the inverse of a diagonally dominant matrix”, Math. Comp. (to appear)
2.	N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996
3.	J. W. Demmel, N. J. Higham, R. S. Schreiber, “Stability of block LU factorization”, Numerical Linear Algebra with Applications, 2 (1995), 173–190
4.	Kh. D. Ikramov, “O blochnom analoge svoistva diagonalnogo preobladaniya”, Vestnik Mosk. un-ta. Seriya 15. Vychisl. mat. kibernet., 1983, no. 4, 52–55