Applications Of Numerical Methods Based On Improved Artificial Fish-Swarm Algorithm

The numerical method is a mathematics branch, whose object of study is to solve the numerical methods and the related theories of each mathematics question using the computer. The content includes numerical solution of nonlinear equation (group) function, solving matrix eigenvalues and solving the real roots of rolynomials and so on. So far, there have been many problems in traditional numerical computational methods. For example, traditional algorithms have sensitive issue of the initial point in computing roots of rolynomials, which can affect the character of solution directly when the initial point is not suitable. Traditional algorithm which is used solving matrix eigenvalues exist some disadvantage such as the speed of calculation slowly, the accuracy lowly, even not convergent and so on. Traditional numerical nonlinear equation (group) function has complicated calculation and steps, furthermore, has some limitations. In view of questions about traditional numerical methods, this paper tries to use improved artificial fish-swarm algorithm to overcome the problems of the classical algorithms.Artificial fish-swarm algorithm (AFSA) is a new swarm intelligence algorithm which was proposed in recent years. It is a novel method to search global optimum. AFSA has many advantages, for example, it has low request in setting objective function, the initial point and parameters. Furthermore, it has the characteristics of evolution algorithms, such as autoadaptive search, global convergence and robustness and so on. By further research, we find that AFSA has some disadvantages although it has many good characteristics. In view of questions about these disadvantages, this paper proposes some ways to improve AFSA, then, use these new ways to solve the problem of numerical methods. This article mainly gets such results as below:(1) Research on how to combine AFSA with traditional algorithms such as BFGS algorithm, Powell algorithm and Hooke-Jeeves algorithm, the aim is to improve local search and the speed convergence.(2) Research on how to use the improved AFSA to solve matrix eigenvalues, so provide a new method for solving matrix eigenvalues.(3) Research on how to use the improved AFSA to solve roots of rolynomials so provide a new method for solving roots of rolynomials.(4) Research on how to use the improved AFSA to solve nonlinear equation (group) function, so provide a new method for solving nonlinear equation (group) function.