近似方法

Base vectors are selected for formulating the nonlinear mapping. An approximate explicit expression is formed by using the Nystrm method for nonlinear mapping which is not available originally. The data in the nonlinear input space is mapped into some linear feature subspace and fisher linear discriminant analysis is computed for the mapped data.

首先提取基向量；然后采用Nystrm方法，以基向量为训练样本，将形式未知的非线性映射近似表达为已知形式的非线性映射，这种近似的非线性映射将变量由非线性的输入空间转换到线性的特征子空间；最后对映射数据进行线性Fisher判别分析。

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 parallel line approximation -a new method for The approximation of demagnetizing field in magnetic-film of single domain is presented.

对磁记录中使用的磁阻传感器的磁阻效应进行了定量分析，并提出了一种新的单畴磁膜退磁场的近似计算方法──平行线近似。

Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the Poincare-Lindstedt method, are discussed in detail through a Duffing oscillator with delayed velocity feedback. It is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. An ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution.

其次，以一具有时滞速度反馈的Duffing系统为例，研究了经典摄动法如多尺度法，Poincaré-Lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。

The new method is based on the approximate expression of phase angle in terms of ray angle.

本文基于以射线角近似表示相角的思想，提出了一种弱各向异性条件下，群速度射线角近似表示的新方法。

The two methods of model simplification are presented for large scale systems, they are the least square approximation and the rational fraction approximation.

本文针对大系统的频域模型简化提出了两种方法：最小二乘近似法和有理分式近似法。

By using testing functions to make comparative research on the precision of approximate models which were built by RBF under the condition of different sample amounts and different kernel function types, a conclusion was drawn: the model quality built by Reciprocal Multiquadric RBF as kernel function was highest when the sample amout was big, and the model quality built by Gaussian RBF as kernel function was highest when the sample amount was small.

运用测试函数对在不同样本数量与不同核函数形式下所建立的近似模型的精度进行对比研究，得出逆多二次函数与高斯函数作为核函数分别在大样本和小样本情况下精度最高的结论，并验证了径向基函数近似模型方法能够兼顾效率与精度。

First introduced the lattice-value information systems knowledge, and to partial order for the basis has been a new relationship: advantage, given the reduction and the core, the concept of simplifying the classification of features, it is also given on the approximation, and the approximate reduction of matrix determined theorem and the concept of identification, the final adoption of specific reduction of examples to illustrate this method is effective.

首先介绍了格值信息系统的相关知识，并以偏序关系为基础得到了一种新的关系：优势关系，给出了约简和核心，简化了概念的分类特征，也给出了上近似、下近似及约简的判定定理和辨识矩阵的概念，最后通过具体的例子说明这种约简方法是有效的。

The convergence by use of ellipsoid function is more quickly than that by use of spherical functions as basic function.

提出了基于椭球函数适配的最小能量误差近似的声全息变换方法，解决了拉长体声源声场重建时，采用球函数适配近似收敛性差的问题。

Secondly, method of Taylor series is used to approximate the slow manifold and the O approximation of the slow manifold is given; slow dynamics such as saddle node bifurcation which has been proven to be the same as that for the full system is analyzed; at the same time, fast dynamics including bifurcation conditions and domain of attractor of the stable equilibrium are also analyzed; the attracting region which consists of the stable manifold of the unstable equilibrium and stable equilibrium is given; we found that when the inner flux decay increases, the domain of attractor is enlarged.

首先，给出了电力系统SMIB模型的时间尺度分解，得到标准的奇异摄动模型；其次，利用幂级数方法，给出了慢流形的O近似M〓，分析了在慢流形M〓上的慢动态，得到了慢子系统的鞍结分支值，并证明此分支值与原系统的鞍结分支值相同；分析了快子系统的平衡点和全局分支的存在条件，给出由不稳定平衡点的稳定流形与稳定平衡点形成的吸引域；并研究内部电压对稳定域的影响，发现稳定域随内部电压增加而扩大；最后给出整个系统的稳定平衡点的近似吸引域。

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。