In the past paper the authors developed the design method for determining the gains of PID controller of Smart Helmholtz Resonator by using Response Surface Method and optimization analysis. This method is the original method by the authors and the details are described in the authors' papers. There, it was concluded that the desired resonance frequency of the resonator can be obtained quite accurately by using the gains from the analysis. However, it was shown that there is the error due to the optimization analysis from error analysis. When using optimization analysis, accuracy and calculation cost become key problems. In order to improve this fact it is needed to develop the more accurate method. In this paper it is proposed to utilize Artificial Neural Network (ANN) to improve the accuracy of the obtained resonance frequency. From the numerical simulation it is confirmed that the mapping between the integral gain K_I and the resonance frequency can be constructed very well by using Holographic Neural Network(HNN) and the accuracy of the testing is improved by selecting the input and output of the HNN properly. Namely, the mapping between a single input variable and multiple output variables cannot be constructed correctly, so the mapping between a single input variable and a single output variable is adopted. Moreover, it is found that the relationship between the resonance frequency of the resonator and the integral gain of PID controller is linear under the certain condition by doing simulation. And it is confirmed that the smart Helmholtz resonator is stable in the frequency range adopted in this simulation.

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  Recently performance of IC factorization preconditioning with Inverse-based Dropping has been reported. In that paper, it turned out that the ib_IC factorization of CG method is very effective in view of stability of convergence. In our paper, we make ib_IC factorization preconditioning more efficient using variable parameter of α for diagonal entries of matrix. Moreover, we adopt the MRTR method as the solver of linear systems. This paper will make clear significant characteristics of the proposed accelerated variable type of ib_IC factorization through many numerical experiments.

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  Robust IC decomposition proposed by Ajiz et al. is often used as a useful preconditioning of the CG method. It prevents breakdown during IC decomposition procedure by means of modification for diagonal entries. Moreover, we have devised Crout version of ILU decomposition for efficient solution of nonsymmetric linear systems. In this paper, we consider to restrain over-estimated compensation for diagonal entries based on the concept of Crout version of ILU decomposition for gaining efficient RIC preconditioning. Numerical experiments indicate that the proposed revised RIC decomposition works well as compared with the conventional RIC decomposition.

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  Recently, as a robust precondition of the CG method, RIC, RIC2S decompositions have been remarked and often used in a variety of analytic field. These decompositions outperform in both robustness and convergence rate of the CG method. The robustness causes increase of computation cost in the con-struction of preconditioner matrix and the number of parameters to be adjusted. In this paper, a concept of safety constant is introduced into the RIC2S decomposition. Through numerical experiments, we make clear relationship between test matrices and safety constant used in the revised RIC2S decomposition.

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