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In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

Newton's method, no conditions iterative control!

牛顿法计算程序，迭代没有条件控制！

E. , extended ∑Δ-STAP approach for HBSR is analyzed in detail. Chapter 7 studies the inverse QR iterative algorithm based on nonhomogeneity detection.

第六章研究、分析了一种适于直升机载战场侦察雷达杂波抑制的实用方法—扩展的∑Δ-STAP方法。

The whole contents is divided into five chapters. In chapter 1, as the beginning of this paper, we offered some relative knowledge, such as the cone theory and semi-order method in nonlinear functional analysis. Moreover, we established a new fixed point theorem of the mixed monotone iterative operator.

全文共分成五章：第一章作为准备知识给出了本文要用到的相关知识内容，其中包括非线性泛函分析中的锥理论及半序方法，并建立了新的混合单调算子不动点定理。

After reducing the problem to a nonlinear ill-posed operator equation,Newton type iterative methods were considered.

把问题归结为一个非线性不适定的算子方程后，考虑该方程的Newton型迭代方法。

By adding the nonmembership degree parameter to the partition matrix 〖WTHX〗U〖WTBZ〗 and objective function, the fuzzy cmeans clustering algorithm is improved. Furthermore, the iterative reasoning formula and the algorithm description are presented. Thus the technique ascribes the clustering to a linear restricted programming issue, which is applied to the status of vast samples.

通过增加非隶属度参数对模糊c〖CD*2〗均值(fuzzy cmeans， FCM)聚类算法中的模糊划分矩阵〖WTHX〗U〖WTBZ〗和目标函数进行改造，进而给出迭代推导公式和算法描述，把聚类归结为一个带约束的线性规划问题，适用于大数据量的情况。

GMRES is one of the most popular iterative methods for the solution of big nonsingular nonsymmetric linear systems.

GMRES方法是目前求解大型稀疏非对称线性方程组最为流行的一种迭代方法。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

Iterative method with numerical integration, error under their control, using Newton iteration method.

详细说明：用迭代法计算数值积分，误差自己控制，用牛顿迭代法实现。

In order to describe the random-like feature of chaotic signal, the statistical analysis method for discrete time chaos system is studied. A domain iterative algorithm for numerical estimation of the invariant probability distribution is presented, which is the foundation for the statistical analysis and processing of chaotic signal.

针对混沌系统的随机性特征，本文研究了离散时间混沌系统的统计分析方法，并给出了一种基于Frobenius-Perron算子的区间迭代算法用于混沌映射不变分布的数值求解，该方法在样本数较少时，仍可以获得不变分布的良好估计，为混沌信号进一步的统计分析和处理奠定了基础。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。