逼近

The approximation error is defined as the integral of the minimum distance between each surfel on the original model and the fitting surface.

算法中的逼近误差定义为原始模型各面元到拟合曲面最小距离的积分。

Numerical results show that when the parameter is small enough a global minimum point can be always found with this method.

它的特殊情况是带箱约束的非凸二次规划，对这一情况已经提出了几种逼近方法[5，6] 。

As expected, the results show that GA cannot identify the high order building block problems. Also, the problem for mixing and juxtaposing of building blocks is analyzed. The study suggests that simple selection and crossover require the help of additional operators if fast, efficient processing is desired.

由Holland首先提出的基本遗传算法是研究最为广泛的进化计算算法之一，其基本理论依据是模式定理和"构造块"假设理论，但理论和应用表明GA中的重组操作常造成构造块破坏，导致算法容易早熟逼近局部。

Furthermore, we will discuss the corresponding decay rates problem when the viscous term tends to zero.The first part is about the local existence. We will regularize the equations by the standard mollifier to get the approximate solutions . Then by making uniform estimates to the approximate solutions and by passing to the limit, we obtain the local existence for the above problem.

我们主要研究了此方程组古典解的局部存在性，爆破准则以及通过粘性消失方法来研究如上方程组的局部存在性和收敛率问题，主要结论有：(1)解的局部存在性利用光滑子对方程组进行正则化，从而得到原方程组的逼近解。

In Chapter 3,almost monotone approximation isproposed for nonlinear two-point boundary value problems.

在第三章，我们提出了非线性两点边值问题的几乎单调逼近。

Key words:Almost monotone approximation,Boundary value problems,Non-linear elliptic systems

在第五章，我们提出了具有拟单调性的非线性椭圆型方程组边值问题的几乎单调逼近。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

Second order differential inclusion; boundary condition; usc multivalued map; fixed point; monotone map; Yosida approximation; solution tube; upper-lower solutions; critical point; PS-condition; C-condition; Sobolev space

基础科学，数学，数学分析二阶微分包含；集值边界；上半连续集值映照；不动点；单调算子； Yosida逼近；解管道；上下解；临界点； PS-条件； C-条件； Sobolev空间

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

The approximation keeps some important geometric features of the original curve such as monotonicity,convexity and G1 continuity.

逼近曲线保持了原始曲线的一些重要几何性质，如单调性，凹凸性，G1连续性。

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。