The method is initialization independent and can provide a mathematical and computational guarantee that all solutions of an nonlinear equation are enclosed . " if interval newton algorithm can not find any solution , it can be concluded that there is no solution in the given interval vector 由于能自动处理舍入误差，区间牛顿法不仅能够在理论上，而且能够在计算上保证找到非线性方程组的所有解；若使用区间牛顿法不能找到任何实数解，则可断定在给定的区间向量范围内方程组无解。
One of its most important applications is to improve the optimization algorithms by evaluating the relevant derivatives information efficiently the aim of the work includes : to establish and study new algorithms - - cf - pcg algorithrns with ad ; to establish and study the extended cf - pcg algorithm ( ecfpcg ) . cf - pcg algorithms with ad is proposed on the basis of cf - pcg algorithms with sd , in addition to replace sd with ad , there are other significant modification to the algorithms . the results by theoretical analysis and numerical experiments implicate that cf - pcg algo - rithm with ad is an improvement to newton method with ad 论文首次将自动微分应用于牛顿- pcg型算法，构造了新算法，并从理论上比较了新算法与牛顿法的效率，证明了新算法的效率严格大于牛顿法的效率，而且新算法与牛顿法的效率比分别是问题维数n和目标函数复杂性的严格单调递增函数，当n趋于无穷大时，这个效率比的下界以ln ( n ) ln2的速率趋于无穷大。
Abstract : in this paper we establish a structure analysis model and a structure optimization design model for the outer ring of three - axis simulating table . via quasi - newto nmethod , which is based on characteristic model , optimization design is accomplished , and the scheme thereof is concluded within constraints of first - order natural frequency and static deformation 文摘:建立了某三轴仿真转台的外框的结构分析模型和结构优化设计模型，利用基于性态模型的拟牛顿法对其进行了优化设计，得出了在一阶固有频率和静态变形约束下的最优方案。
Interval newton algorithm is used extensively in the calculation of chemical engineering such as the determination of phase stability , reactive azeotropes , robust process simulation , reliable parameter estimation , etc . all of these results show that interval newton algorithm is suitable to solve most kinds of nonlinear equation successfully 由于区间牛顿法强壮的全局收敛性和同时求得多个解的能力使得区间牛顿法广泛地应用在化工计算领域，如：相稳定性分析、反应共沸物的判断及组成确定、稳态过程模拟、参数估计等等。
