The Software Design Of Simplex Constructing Algorithm For Optimal Design And The Application Research On Fractal Simulation System

The theory and application of optimal design is a statistic branch which grew rapidly in recent years. It is an effective statistics tool for the establishing of mathematical model and the obtaining of optimum processing condition of scientific experiment. It is widely used in many fields such as mining, metallic material, ferrous metallurgy, automatic control, mechanism manufacture, chemical industry, etc, and has obtained interesting result. So the author choices the computer constructing and software design of optimal design as research subject, combines ihe theory of chaotic fractal with the theory of optimal design, which creates a new researching area.The modified simplex algorithm and software design of constructing D-optimal design are proposed by studying the numerical constructing algorithm and symmetric algorithm of D-optimal design. The D-optimal designs of multi-component mixture regression models and high-order mixture regression models with logarithmic terms have been constructed by the new algorithm. At the same time, the Dn-optimal exact designs of multi-component mixture regression models with logarithmic terms have been constructed by the means of Wynn's exchange algorithm. The new constructed optimal designs are used in the welding process and the regression analysis is given. The chaotic characteristic is described in detail by analyzing the Lyapunov exponent for the regression equation and test result.The modified simplex method has been further used in the constructing of M-J sets, and the simplex rotational symmetry escape time algorithm is proposed that combines the simplex algorithm with the classic escape time algorithm, which is called simplex fractal constructing algorithm for short, and a great deal of M-J set fractal images are drawn out by the new algorithm.By analyzing the general M-J set intensively, the inner geometry characteristic is found. The express of "Mandelbrot set is compact dictionary of Julia set" has been proved, and the method of finding the geometry characteristic from M-J sets is given.