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Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices

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  • Orera, H.
  • Peña, J.M.

Abstract

For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly diagonally dominant matrix. Numerical examples and comparisons with other bounds are included. The scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a Nekrasov matrix. These error bounds can improve considerably other previous bounds.

Suggested Citation

  • Orera, H. & Peña, J.M., 2019. "Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 119-127.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:119-127
    DOI: 10.1016/j.amc.2019.04.027
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    References listed on IDEAS

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    1. Liu, Jianzhou & Zhang, Juan & Zhou, Lixin & Tu, Gen, 2018. "The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 251-263.
    2. Szulc, Tomasz & Cvetković, Ljiljana & Nedović, Maja, 2015. "Scaling technique for Partition-Nekrasov matrices," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 201-208.
    3. Lei Gao & Chaoqian Li & Yaotang Li, 2014. "A New Upper Bound on the Infinity Norm of the Inverse of Nekrasov Matrices," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, June.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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