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    This study introduces a novel zeroing neural network (ZNN) model, ZNNGOI, to compute time-varying generalized-outer (G-outer) inverses. The ZNNGOI model effectively addresses time-varying matrix challenges and shows comparable performance to standard ZNN methods.

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    Area of Science:

    • Numerical analysis
    • Matrix theory
    • Computational mathematics

    Background:

    • Time-varying (TV) matrix generalized inverse calculation is crucial for diverse scientific and engineering fields.
    • Existing methods face challenges in efficiently computing TV matrix inverses.
    • Generalized-outer (G-outer) inverses are a subclass of inner inverses with specific applications.

    Purpose of the Study:

    • To develop a novel method for constructing time-varying generalized-outer inverses (TV-GOIs).
    • To introduce a new zeroing neural network (ZNN) model, ZNNGOI, for computing TV-GOIs.
    • To evaluate the performance of the ZNNGOI model in solving TV matrix problems.

    Main Methods:

    • Utilizing the zeroing neural network (ZNN) process for dynamic system solutions.
    • Developing a novel ZNN model, termed ZNNGOI, specifically for TV-GOI computation.
    • Conducting numerical simulations to validate the ZNNGOI model's efficacy.

    Main Results:

    • The ZNNGOI model successfully computes TV-GOIs.
    • Numerical simulations demonstrate excellent performance of the ZNNGOI model.
    • The ZNNGOI model shows performance comparable to standard ZNN for pseudoinverse computation in linear TV matrix equations.

    Conclusions:

    • The ZNNGOI model represents a novel and effective approach for calculating TV-GOIs.
    • The ZNNGOI model offers a robust solution for time-varying matrix challenges.
    • This research contributes a new tool for solving linear TV matrix equations and localization problems.