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Entrywise relative perturbation theory for nonsingularM-matrices and applications

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Abstract

This paper establishes a new entrywise relative perturbation result for the inverse of a nonsingularM-matrixA. It is shown that a version of Gaussian elimination with one step of iterative refinement solves the systemAx =b, whereb is nonnegative, with small entrywise relative error. IfA is tridiagonal, the Gaussian elimination alone suffices.

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, 200433, Shanghai, People's Republic of China

    Xue Jungong & Jiang Erxiong

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  1. Xue Jungong
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  2. Jiang Erxiong
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Jungong, X., Erxiong, J. Entrywise relative perturbation theory for nonsingularM-matrices and applications. Bit Numer Math 35, 417–427 (1995). https://doi.org/10.1007/BF01732614

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  • DOI: https://doi.org/10.1007/BF01732614

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