Accurate and efficient $$\textit{LDU}$$ LDU decomposition of almost diagonally dominant Z-matrices

Abstract

For a class of $$n\times n$$ nonsingular almost row diagonally dominant $$Z$$ -matrices and given adequate parameters, an efficient method to compute its $$\textit{LDU}$$ decomposition with high relative accuracy is provided. It adds an additional cost of $${\fancyscript{O}}(n^2)$$ elementary operations over the computational cost of Gaussian elimination. Numerical examples illustrate that the obtained $$\textit{LDU}$$ decompositions are rank revealing, and comparisons with alternative procedures are included.