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The High Relative Accuracy of Computations with Laplacian Matrices

Author

Listed:
  • Héctor Orera

    (Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain
    These authors contributed equally to this work.)

  • Juan Manuel Peña

    (Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain
    These authors contributed equally to this work.)

Abstract

This paper provides an efficient method to compute an L D U decomposition of the Laplacian matrix of a connected graph with high relative accuracy. Several applications of this method are presented. In particular, it can be applied to efficiently compute the eigenvalues of the mentioned Laplacian matrix. Moreover, the method can be extended to graphs with weighted edges.

Suggested Citation

  • Héctor Orera & Juan Manuel Peña, 2024. "The High Relative Accuracy of Computations with Laplacian Matrices," Mathematics, MDPI, vol. 12(22), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3491-:d:1516956
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