COMPONENTWISE ANALYSIS OF DIRECT FACTORIZATION OF REAL SYMMETRICAL AND HERMITIAN MATRICES

We derive componentwise error bound for the factorization H = GJC(T), where H is a real symmetric matrix, G has full column rank, and J is d iagonal with +/- 1's on the diagonal. We also derive a componentwise f orward error bound, that is, we bound the difference between the exact and the computed factor G, in the cases where such a bound is possibl e. We extend these results to the Hermitian case, and to the well-know n Bunch-Parlett factorization. Finally, we prove bounds for the scaled condition of the matrix G, and show that the factorization can have t he rank-revealing property. (C) 1998 Elsevier Science Inc.