BIT Numerical Mathematics

, Volume 54, Issue 2, pp 343–356 | Cite as

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

  • A. Barreras
  • J. M. Peña


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.


\(\textit{LDU}\) decomposition Rank revealing decomposition Accuracy Z-matrices Almost diagonal dominance 

Mathematics Subject Classification (2000)

65F35 65F30 65F05 15A23 



The authors wish to thank the anonymous referees for their valuable suggestions to improve the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department Applied Mathematics/IUMAUniversidad de ZaragozaZaragozaSpain

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