Chansangiam, Pattrawut

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Chansangiam, Pattrawut
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Chansangiam, P.
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pattrawut.ch@kmitl.ac.th

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    Gradient iterative method with optimal convergent factor for solving a generalized sylvester matrix equation with applications to diffusion equations
    (2020-10-01)
    Boonruangkan, Nunthakarn
    ;
    Chansangiam, Pattrawut
    We introduce a gradient iterative scheme with an optimal convergent factor for solving a generalized Sylvester matrix equation ∑<sup>p</sup>i=1<sup>A</sup> i XB<inf>i</inf> = F, where A<inf>i</inf>, B<inf>i</inf> and F are conformable rectangular matrices. The iterative scheme is derived from the gradients of the squared norm-errors of the associated subsystems for the equation. The convergence analysis reveals that the sequence of approximated solutions converge to the exact solution for any initial value if and only if the convergent factor is chosen properly in terms of the spectral radius of the associated iteration matrix. We also discuss the convergent rate and error estimations. Moreover, we determine the fastest convergent factor so that the associated iteration matrix has the smallest spectral radius. Furthermore, we provide numerical examples to illustrate the capability and efficiency of this method. Finally, we apply the proposed scheme to discretized equations for boundary value problems involving convection and diffusion.
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    Convergence analysis of a gradient iterative algorithm with optimal convergence factor for a generalized sylvester-transpose matrix equation
    (2021-01-01)
    Boonruangkan, Nunthakarn
    ;
    Chansangiam, Pattrawut
    Consider a generalized Sylvester-transpose matrix equation with rectangular coefficient matrices. Based on gradients and hierarchical identification principle, we derive an iterative algorithm to produce a sequence of approximated solutions with a reasonable stopping rule concerning a relative norm-error. A convergence analysis via Banach fixed-point theorem reveals the sequence converges to a unique solution of the matrix equation for any given initial matrix if and only if the convergence factor is chosen appropriately in a certain range. The performance of algorithm is theoretically analysed through the convergence rate and error estimations. The optimal convergence factor is chosen to attain the fastest asymptotic behaviour. Finally, numerical experiments are provided to illustrate the capability and efficiency of the proposed algorithm, compared to recent gradient-based iterative algorithms.