In this paper, for the implicit complementarity problem, it is shown that the solution’s sign patterns can be calculated via solving a linear system under some assumptions. Next, Newton iteration is applied to a equivalent nonlinear equation with quadratic convergence and the non-singularity of the Jacobian is discussed. Moreover, a superlinearly convergent hybrid method is established by combining an existing globally convergent iteration and the Newton iteration. Numerical examples show that the proposed methods have higher precision and converge faster than some existing methods.

中文翻译：

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基于符号分析的一类隐式互补问题的超线性收敛方法

在本文中，对于隐式互补问题，表明可以通过在某些假设下求解线性系统来计算解的符号模式。接下来，将牛顿迭代应用于具有二次收敛的等效非线性方程，讨论雅可比行列式的非奇异性。此外，结合现有的全局收敛迭代和牛顿迭代，建立了超线性收敛混合方法。数值例子表明，所提出的方法比现有的一些方法具有更高的精度和更快的收敛速度。