迭代法

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

This paper has improved some conventional algorithms and presents the weighting iterative improved algorithm and PSD-PCG algorithm, basing on the analysis of ill-conditioned linear system of equations characteristic and origin.

本文在分析了病态线性方程组的特点和成因的基础上，对一些传统的算法进行了改进，给出了加权迭代改善法和PSD—PCG法。

A new single image super-resolution reconstruction algorithm is presented based on projection. Using the Kronecker product of two matrices, the vector based observation model is converted to an equivalent matrix based model.

目前，已提出了各种图像超分辨率算法，其中较经典的有频域法、MAP方法、极大似然估计法、凸集投影P(CS方法以及基于相机成像模型的迭代算法[3]，近年又发展了基于小波l_4_、基于学习及基于识别等的新算法。

In this system,arc length of the curve between two points is calculated by Simpson method,and then observer's position and orientation at every frame are deduced by bisection.

通过Simpson法计算两点之间曲线弧长，二分法迭代得到观察者每一帧时所处的视点和视角。

In Chapter 4, a symmetric triangular partitioned secant method for solving large scale sparse unconstrained optimization problems is constructed, which is a combination of a secant method and a finite difference method, and depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix; it reduces the number of gradient evaluations required by Powell and Toints algorithm (the indirect lower triangular substitution algorithm) by one at every iterative step.

此算法是基于稀疏Hesse阵的下三角部分的列的相容分划的基础上建立起来的，把割线法和有限差分法有机的结合在了一起，在每次迭代中，把由Powell和Toint的算法所需要的梯度赋值次数减少了一。

This paper used the Savitzky-Golay filter method to reconstruct the MODIS 16d NDVI time-series product of Ruoergai plateau wetland from 2000 to 2009, and the results were compared with the other two methods— Mean Value Iteration filter and Fourier method.

本文利用Savitzky-Golay滤波方法对若尔盖高原湿地区2000年至2009年MODIS 16天最大值合成的NDVI时间序列数据进行了重构，并与中值迭代滤波法、傅里叶变换法进行了比较。

Parameters simplification of dynamic relaxation method is an improvement of the traditional method, and the increment of iteration is so small that this promoted method is worthy of further studying.

参数简化的动力松弛法是对传统动力松弛法的改进，而计算迭代次数比原来提高不多，因此，本方法值得尝试与进一步研究改进。

The normal transformation polynomial is used by some researcher in practical probabilistic analysis in structural or civil engineering; especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved.

本论文提出了两种样本点选取策略，即方向余弦策略和有限步长策略，对响应面法进行改良；本方法一次性拟合响应面方程，避免了常规响应面法的复杂迭代运算，且对高非线性问题有较好的适用性。

This paper improves the iterative format of the symmetric successive overrelaxation PCG method,as a result the computation is reduced by 8%～50%.This paper also presents some key subroutines for application of the SSOR PCG method to the solution of finite element equations.

本文改进了对称逐步超松驰预处理共轭梯度法的迭代格式，可节省计算量8％～50％，并给出应用SSORPCG法求解有限元方程组时的几个关键子程序。

The detailed algorithm on analyzing cracks exploration inside blocks is: enriched approximations which describe singular crack tips fields and discontinuous crack faces are employed under the Partition of Unity theory; the enriched nodes surrounding crack tips or faces are respectively mapped with corresponding enriched degrees of freedom, and the solution of all these degrees of freedom is uniformly proceeded by the implicit iteration algorithm of DDA, then fracture and breakage of DDA blocks can be analyzed. The numeric examples show this algorithm is rational and efficient.

为此建立的无网格法裂纹扩展分析算法，采用满足单位分解条件的特殊增强型函数表达裂纹周围应力场的非连续、奇异特性，将对应的扩展自由度动态映射到裂纹周围的节点上，统一按DDA法隐式迭代方式求解，实现块体裂纹扩展和强度分析，相关算例结果显示该算法是合理有效的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。