Research On Numerical Methods Based On PSO

In recent years, the electronic computers and its applications developed greatly, the experimental technique has been surpassed and replaced by the scientific computing gradually in the multitudinous domains. The scientific computing was the third method of the scientific research, and it was more and more important. One of mathematics' branch is the computational method, its object of study is to solve the numericalmethods and the related theories of each mathematics question using the computer. The content includes numerical solution of nonlinear equation and nonlinear equation group function, numerical integration and numerical differentiation, digital approximation (interpolation and fitting), and so on. Particularly, with the appearance of the new computational intelligence technology of late years, the research related to numerical computation suited for computational intelligence method is becoming extremely essential and urgent. In traditional numerical computational methods there are many problems. For example, traditional Eigenvalues methods are difficult to find complex Eigenvalues, traditional numerical integral methods are very difficult to obtain high accuracy and low complexity and so on, In the article we use PSO of the computational intelligence technology to study the related questions of traditionalnumerical computational methods.Aiming at the disadvantage of traditional numerical methods, the main task of this article is using the characteristics of PSO, such as global convergence, autoadaptive search and robustness and so on, to solve problems of traditional numerical methods. The proposed numerical methods based on the PSO here mainly include numerical integral, solving Eigenvalues and Eigenvectors and interpolation polynomial and so on, which offer some references and some practical application background in order to improving traditional numerical methods.