Backward error bounds for 2×2 linear systems arising in the diagonal pivoting method

Abstract

Matrix factorizations such as LU, Cholesky and others are widely used for solving linear systems. In particular, the diagonal pivoting method can be applied to symmetric and indefinite matrices. Floating-point arithmetic is extensively used for this purpose. Since finite precision numbers are treated, rounding errors are involved in computed results. In this paper rigorous backward error bounds for 2×2 linear systems which arise in the factorization process of the diagonal pivoting method are given. These bounds are much better than previously known ones.