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
We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach spaces.In earlier studies,hypotheses on the Fréchet derivative up t...We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach spaces.In earlier studies,hypotheses on the Fréchet derivative up to the fifth order of the operator un-der consideration is used to prove the convergence order of the method although only divided differences of order one appear in the method.That restricts the applicability of the method.In this paper,we extended the applicability of the fifth order Traub-Steffensen-Chebyshev-like composition without using hypotheses on the derivatives of the operator involved.Our convergence conditions are weaker than the conditions used in earlier studies.Numerical examples where earlier results cannot apply to solve equa-tions but our results can apply are also given in this study.展开更多
The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ...The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.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.
文摘We present the local convergence analysis of a fifth order Traub-Steffensen-Chebyshev-like composition for solving nonlinear equations in Banach spaces.In earlier studies,hypotheses on the Fréchet derivative up to the fifth order of the operator un-der consideration is used to prove the convergence order of the method although only divided differences of order one appear in the method.That restricts the applicability of the method.In this paper,we extended the applicability of the fifth order Traub-Steffensen-Chebyshev-like composition without using hypotheses on the derivatives of the operator involved.Our convergence conditions are weaker than the conditions used in earlier studies.Numerical examples where earlier results cannot apply to solve equa-tions but our results can apply are also given in this study.
文摘The author provides a finer local as well as semilocM convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space （m ≥ 1 a natural number）.
