Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices (Q644775)

The authors develop a structured perturbation theory for the LDU factorization of (row) diagonally dominant matrices of order \(n\) and then use this theory to prove rigorously that an algorithm of \textit{Q. Ye}, [Math. Comput. 77, No. 264, 2195--2230 (2008; Zbl 1198.65077)] computes the factors \(L\), \(D\) and \(U\) with relative errors less than \(14n^{3}{\mathbf u}\), where \({\mathbf u}\) is the unit roundoff of the computer. The relative errors for \(D\) are componentwise and for \(L\) and \(U\) are normwise with respect to the max norm \({\|A\|_M = \max_{ij} |a_{ij}|}\).