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

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Department Applied Mathematics/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    A. Barreras & J. M. Peña

Authors
  1. A. Barreras
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  2. J. M. Peña
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Corresponding author

Correspondence to A. Barreras.

Additional information

Communicated by Michiel Hochstenbach.

Research partially supported by the Spanish Research Grant MTM2012-31544, by Gobierno de Aragón and Fondo Social Europeo.

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Barreras, A., Peña, J.M. Accurate and efficient \(\textit{LDU}\) decomposition of almost diagonally dominant Z-matrices. Bit Numer Math 54, 343–356 (2014). https://doi.org/10.1007/s10543-013-0461-1

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  • DOI: https://doi.org/10.1007/s10543-013-0461-1

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