In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximat...In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.展开更多
An analytical method was proposed dielectric properties for particulate composites. to calculate effective linear and nonlinear The method is based on an approximate solution of two-particle interaction problem, and i...An analytical method was proposed dielectric properties for particulate composites. to calculate effective linear and nonlinear The method is based on an approximate solution of two-particle interaction problem, and it can be applied to relatively high volume concentration of particles （up to 50%）. Nonlinear dielectric property was also examined by means of secant method. It is found that for low applied electric filed the proposed method is close to Stroud and Hui＇s method and for high applied electric filed it is close to Yu＇s method.展开更多
基金Supported by the Qianjiang Rencai Project Foundation of Zhejiang Province (J20070288)
文摘In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.
基金Project supported by the National Natural Science Foundation of China (No.10325210)
文摘An analytical method was proposed dielectric properties for particulate composites. to calculate effective linear and nonlinear The method is based on an approximate solution of two-particle interaction problem, and it can be applied to relatively high volume concentration of particles （up to 50%）. Nonlinear dielectric property was also examined by means of secant method. It is found that for low applied electric filed the proposed method is close to Stroud and Hui＇s method and for high applied electric filed it is close to Yu＇s method.
