Numerische Mathematik

, Volume 38, Issue 2, pp 179–192 | Cite as

On theLU factorization ofM-matrices

  • Richard S. Varga
  • Da-Yong Cai


In this paper, we give in Theorem 1 a characterization, based on graph theory, of when anM-matrixA admits anLU factorization intoM-matrices, whereL is a nonsingular lower triangularM-matrix andU is an upper triangularM-matrix. This result generalizes earlier factorization results of Fiedler and Pták (1962) and Kuo (1977). As a consequence of Theorem 1, we show in Theorem 3 that the conditionx T A0 T for somex>0, for anM-matrixA, is both necessary and sufficient forPAP T to admit such anLU factorization for everyn×n permutation matrixP. This latter result extends recent work of Funderlic and Plemmons (1981). Finally, Theorem 1 is extended in Theorem 5 to give a characterization, similarly based on graph theory, of when anM-matrixA admits anLU factorization intoM-matrices.

Subject Classifications

AMS(MOS) 15 A 23 CR: 5.14 


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Richard S. Varga
    • 1
  • Da-Yong Cai
    • 1
  1. 1.Institute for Computational MathematicsKent State UniversityKentUSA

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