A convergence proof is given for the continuous analog of the Newton method for linear semi-positive definite operator equations and convergence rates are obtained.

对半正定线性算子方程考虑了一类连续正则化牛顿方法，给出了收敛证明，得到了收敛率。

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In this paper we present a smoothing Newton method for solving ball constrained variational inequalities. Global and superlinear convergence theorems of the proposed method are established.

研究球形约束变分不等式求解的算法，提出一种光滑化牛顿方法，证明了该方法具有全局收敛性和超线性收敛。

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The Newton iterative method is used in the calculation of entropy density function, by which the non-convergence issue in the calculation for the vertical bearing capacity of piles is solved.

计算熵密度函数时采用牛顿迭代法，从而解决了在分析基桩竖向承载力的可靠度时可能产生的迭代不收敛的情况。

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