Abstract

A modified Trapezoidal Broyden’s method for nonlinear equations is presented. We design and implement an alternative approximation to Jacobian matrix of Trapezoidal Broyden’s method. This method improve the efficiency by reducing the number of iterations required by the Broyden’s method, and solve the problem that the approximate matrix almost singular or singular at some points. The local convergence properties of the new method is presented. Numerical results illustrate that the proposedmethod is efficient and robust.

中文翻译：

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非线性方程的修正梯形布罗伊登方法

摘要

提出了非线性方程的修正梯形布罗伊登方法。我们设计并实现了梯形布洛伊登方法的雅可比矩阵的替代近似。该方法通过减少布罗伊登方法所需的迭代次数来提高效率，解决近似矩阵在某些点几乎奇异或奇异的问题。介绍了新方法的局部收敛特性。数值结果表明所提出的方法是有效和稳健的。