Componentwise backward error analysis of Neville elimination

In this paper, we perform a backward error analysis of Neville elimination whenever there need row exchanges. Componentwise backward error bounds are presented for this elimination procedure applied to any nonsingular matrices. Consequently, it is shown that Neville elimination with two-determinant pivoting proposed by Cortes and Peña (2007) [5] is an excellent method for the triangularization of nonsingular sign regular matrices including totally nonnegative and totally nonpositive matrices, which has a pleasantly small componentwise relative backward error. In particular, a small componentwise relative error bound is also provided for the bidiagonal factorization of totally nonnegative matrices.