On the sensitivity of the LU factorization

Abstract. This paper gives sensitivity analyses by two approaches for L and U in the factor-ization A = LU for general perturbations in A which are sufficiently small in norm. By the matrix-vector equation approach, we derive the condition umbers for the L and U factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting affect the sensitivity of the LU factorization. AMS subject classification: 15A23, 65F35