STABILITY OF BLOCK LU FACTORIZATION

Many of the currently popular 'block algorithms' are scalar algorithms in which the operations have been grouped and reordered into matrix o perations. One genuine block algorithm in practical use is block LU fa ctorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization i s stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be bounded in terms of the condition number kappa(A) and the growth f actor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric pos itive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.