Some New Variants of Cauchy's Methods for Solving Nonlinear Equations

[摘要] We present and analyze some variants of Cauchy's methods free fromsecond derivative for obtaining simple roots of nonlinear equations. The convergenceanalysis of the methods is discussed. It is established that the methods have convergence order three. Per iteration the new methods require two function and one firstderivative evaluations. Numerical examples show that the new methods are comparable with the well-known existing methods and give better numerical results in manyaspects.

[学科分类] 应用数学