Study of numerical analysis via control theory

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This research intended to develop a new solution scheme via filters obtained by modern sampled-data control theory. Since sampled-data control theory processes continuous-time signals via discrete-time models, this approach is expected to develop a new horizon, also in view of the highly successful outcomes in sound and image processing. Nonetheless, while ensured to be effective for linear-time invariant systems, the new scheme was found not to be effective for nonlinear or stiff systems. This is presumed to be due to the time-invariant nature of the system characteristic on which the designed filters are based, and hence those filters are not so effective for computing transients. This leads to the conjecture that one should proceed to a development of time-varying filters. As a byproduct, however, it has been found that such time-invariant filters can be effective in reducing phase distortions by digital processing. Such a characteristic is useful in sound and image processing, and expected to become more effective in the future.