Componentwise analysis of direct factorization of real symmetric and hermitian matrices

Abstract

We derive componentwise error bound for the factorization H = GJG T , where H is a real symmetric matrix, G has full column rank, and J is diagonal with ±1's on the diagonal. We also derive a componentwise forward error bound, that is, we bound the difference between the exact and the computed factor G, in the cases where such a bound is possible. We extend these results to the Hermitian case, and to the well-known Bunch-Parlett factorization. Finally, we prove bounds for the scaled condition of the matrix G, and show that the factorization can have the rank-revealing property.