IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v358y2019icp119-127.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303091
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.027?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhaskar Ray Chaudhury & Jugal Garg & Peter McGlaughlin & Ruta Mehta, 2023. "A Complementary Pivot Algorithm for Competitive Allocation of a Mixed Manna," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1630-1656, August.
    2. Karan N. Chadha & Ankur A. Kulkarni, 2022. "On independent cliques and linear complementarity problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1036-1057, December.
    3. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    4. Parthasarathy T & Ravindran G & Sunil Kumar, 2025. "On Q-tensors," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-13, November.
    5. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    6. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    7. Guo-qiang Wang & Yu-jing Yue & Xin-zhong Cai, 2009. "Weighted-path-following interior-point algorithm to monotone mixed linear complementarity problem," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 435-445, December.
    8. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
    9. G. L. Zhou & L. Caccetta, 2008. "Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 379-392, November.
    10. A. K. Das, 2016. "Properties of some matrix classes based on principal pivot transform," Annals of Operations Research, Springer, vol. 243(1), pages 375-382, August.
    11. Xi-Ming Fang & Zhi-Jun Qiao & Heng-Jun Zhao, 2019. "The Block Principal Pivoting Algorithm for the Linear Complementarity Problem with an M‐Matrix," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    12. Meijuan Shang & Chao Zhang & Naihua Xiu, 2014. "Minimal Zero Norm Solutions of Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 795-814, December.
    13. Massol, Olivier & Rifaat, Omer, 2018. "Phasing out the U.S. Federal Helium Reserve: Policy insights from a world helium model," Resource and Energy Economics, Elsevier, vol. 54(C), pages 186-211.
    14. S. R. Mohan, 1997. "Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 409-423, August.
    15. Diethard Klatte, 2026. "Lipschitz stability for a class of parametric optimization problems with polyhedral feasible set mapping," Computational Management Science, Springer, vol. 23(1), pages 1-25, June.
    16. Thiruvankatachari Parthasarathy & Gomatam Ravindran & Sunil Kumar, 2022. "On Semimonotone Matrices, $$R_0$$ R 0 -Matrices and Q-Matrices," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 131-147, October.
    17. Y. P. Fang & N. J. Huang, 2006. "Feasibility and Solvability for Vector Complementarity Problems1," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 373-390, June.
    18. Xiaojun Chen & Yun Shi & Xiaozhou Wang, 2020. "Equilibrium Oil Market Share under the COVID-19 Pandemic," Papers 2007.15265, arXiv.org.
    19. Dongmei Yu & Huiling Wei & Cairong Chen & Deren Han, 2024. "Scalable Relaxation Two-Sweep Modulus-Based Matrix Splitting Methods for Vertical LCP," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 714-744, October.
    20. Niu, Yi-Shuai & Júdice, Joaquim & Le Thi, Hoai An & Pham, Dinh Tao, 2019. "Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 95-113.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:119-127. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.