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Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

Author

Listed:
  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Javier G. Maimó

    (Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 Valencia, Spain)

  • María P. Vassileva

    (Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Av. Los Procéres, Gala, Santo Domingo 10602, Dominican Republic)

Abstract

Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore–Penrose inverse of a singular square matrix or an arbitrary m × n complex matrix. A Kurchatov-type scheme and Steffensen’s method with memory were developed for estimating these types of inverses, improving, in the second case, the order of convergence of the Newton–Schulz scheme. The convergence and its order were studied in the four cases, and their stability was checked as discrete dynamical systems. With large matrices, some numerical examples are presented to confirm the theoretical results and to compare the results obtained with the proposed methods with those provided by other known ones.

Suggested Citation

  • Alicia Cordero & Javier G. Maimó & Juan R. Torregrosa & María P. Vassileva, 2023. "Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3161-:d:1196951
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    References listed on IDEAS

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    1. Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2015. "A multidimensional dynamical approach to iterative methods with memory," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 701-715.
    2. Cong-Trang Nguyen & Yao-Wen Tsai, 2017. "Finite-Time Output Feedback Controller Based on Observer for the Time-Varying Delayed Systems: A Moore-Penrose Inverse Approach," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, May.
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