逼近

This article makes use of the approximation property of Laguerre orthogonal function series to present a Laguerre function approxima te model of linear dynamic systems.The model eliminates the need for assumption of the plant order and the time delay and approaches unknown systems via estimat ing the Laguerre coefficients on-line.

蒋中摘要：利用Laguerre正交函数序列对空间函数的良好逼近特性，建立了线性动态系统的Laguerre函数近似模型，该模型不需要对象的阶次和时延等结构知识，通过在线辨识对象的 Laguerre系数矩阵，能较好地逼近结构未知系统。

According to the orthonormality of Legendre polynomials in the function approximation theory, the exact boundary of the ball Bézier surface was optimally squarely approximated in polynomial form.

依据函数逼近论中Legendre多项式的正交性，得到了采用多项式形式表示的球域Bézier曲面的精确边界的最佳平方逼近。

In piecewise linear approximation, the promisingapplication of two modes in separable programming and intrinsic limitations are discussed.

在分段线性逼近中，讨论了两种逼近模式在可分离规划中的应用前景和算法内在的局限性。

Using the theory of empirical wavelet transform,linear approximation andnonlinear approximation we establishes the foundation of wavelet compression.

小波的应用的方面，利用经验小波变换、线性逼近和非线性逼近建立了小波压缩的基本理论框架。

There have been a lot of studies this aspect when the exact solution u∈H~2 or u∈H~3. [4], [52] and [50]studied the convergence of conforming linear triangle elements with minimal regularity assumptions u∈H~4, here u is the solutions of the second order elliptic problems. However, their is another vital deficiency of the previous studies, i.e., they relies on the regularity assumption or quasi-uniform assumption on the subdivision of meshes.

对二阶问题，构造了一个新的单元格式，当其精确解具有低正则性时，在不要求网格满足正则假设或拟一致假设的条件下，我们得到了最优误差估计，与[33]相比，我们的证明方法较为简单；对于Stokes问题，研究五节点非协调矩形元对它的逼近，通过引入全新的估计方法，给出了关于速度、压力的超逼近性质。

In elliptic case,the compactness of"convex polyhedrons"is destinedto be true because of the"local Lipschitz continuity of convex functions",whilein parabolic case,we cannot expect convex-monotone functions have such goodproperties as convex functions.

在广义解存在性的证明中，参考椭圆情形由"凸多面体"逼近的思想，我们采用了由一种特殊构造的"凸单调多面体"逼近的途径，但在证明这种凸单调多面体族的紧性时，我们遇到了困难。

The nonlinear items only satisfy the local Lipschitz condition, but not the uniformly Lipschitz condition. The step function is applied to the approximate controllability problem of the corresponding linear system.

这类非线性系统中的非线性项只满足局部Lipschitz条件，于是采用了阶梯函数的方法，对于热传导方程的逼近能控性进行了讨论，得到了线性系统的逼近能控性，并给出了控制的显式表达，而在文献[103]中控制的具体求法是未知的。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

Varnhorn applied the method of approximate approximation to functions which are defined on compact intervals and investigated the error.

Varnhorn给出了一维紧区间上函数的近似逼近方法，而且还可以控制近似逼近的截断误差。

The method of multiple models approximation using self-organizing map neural network is analyzed. The mechanism of this method is different to that of approximation method using other kinds of feedforward neural networks.

针对基于自组织映射神经网络的非线性函数逼近，研究其方法和原理，指出它与一般前向神经网络在逼近原理上的不同。

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。