The Studying Of Solving Algebraic Equation (Groups) Based On Artificial Fish School Algorithm

Solving algebraic equation(groups) and computing the related problems are basic and important. Because there are a great deal of actual problems will translate into solving real roots of algebraic equation(groups) (especially, multivariable nonlinear algebraic equations) in the end, such as engineering technology, economics, information safety and dynamics etc. There is an important significance for analyzing and comprehensive designing of control system to solve algebraic equation which has arbitrary real coefficients; We need to estimate the module of algebraic equation's roots in lots of mathematics theoreticses and practice applying. For example, in the judging of stability of discrete-time control system, in order to improve the veracity of judging, we should have a higher request to the accuracy of estimating to the largest module of roots of algebraic equation, but traditional methods can't do it. Most of traditional methods have some objections, for example, complicated calculation and steps, lower precision, and so on.In recent years, evolution algorithm has attracted lots of researchers of numerous science areas, which has higher adaptability, robustness, parallel and global quality etc., and are used widely in some areas such as function optimization, pattern recognition and image processing etc.. This article studies the application of a new evolution algorithm—artificial fish school algorithm, in solving algebraic equation(groups) and computing the related problems. This evolution algorithm can overcome local extremum and get some global extremums, initial values can be chosen random and carrying out this algorithm doesn't need to know gradient value of the objective function, so it has robustness for the searching area. This article uses artificial fish school algorithm to solve some problems about algebraic equation(groups), and this article mainly get such results as below:(1) The theorem which is used to judge whether all roots of a polynomial are in unit circle is put forward. And artificial fish school algorithm for finding the largest module of roots of an algebraic equation based on the judging theorem is given. Several computer simulation results show that this algorithm is better than other methods which have been put forward.(2) Algebraic equation is declined power using Taylor expansion at zeros of polynomial, and a sequence of algebraic equations is get. Every Taylor expansion zero of algebraic equation sequence is solved by improved artificial fish school algorithm, that is all roots of algebraic equation. Several computer simulation results show that this algorithm has high solving speed, high precision of solution, and it is better than genetic algorithm. Furthermore, this method resolves the problem of solving multiple roots.(3) Sturm theorem is used into designing the food consistence function, and artificial fish school algorithm of determining the place of real roots of algebraic equation with rational coefficients is given. Simulation experiments show that this algorithm is very fast for determining the place of real roots. K -random dividing method which optimizes the real roots isolator interval for finding all real roots of algebraic equation with rational coefficients is proposed. Simulation experiments show that K -random dividing method can find all real roots of algebraic equation quickly; furthermore, the precision of real roots is much higher.(4) Artificial fish school algorithm of solving nonlinear multivariable algebraic equation systems is put forward. The moving condition is improved, and segmented optimization is introduced in this algorithm. Most of traditional methods have complicated calculation and steps, furthermore, have some limitations. But this algorithm has simple algorithm design method, and high self-adaptation. Simulation experiments show that this algorithm is better than genetic algorithm such as faster solving speed and higher precision.