病态函数

Using the potential function method,we turn the illposed inversion problem into goodposed one,and provide the conditions of the edgepreserving potential function.

通过势函数方式将波阻抗反演的病态问题转为良态问题，并且给出了边界保护势函数所具备的条件。

Preliminary numerical results for the Laplace equation and Navier system are presented, and tricky issues associated with these methods, such as the ill-conditioning with the interpolation matrix and effect of shape parameter, are investigated.

文中给出了Laplace方程和Navier方程组的数值结果，考察了插值矩阵的病态性以及径向基函数中形参数的影响。

An improved Schur multistep method has been presented for controlling error severely cumulating and increasing computational accuracy.

为解决刚性问题中导函数项的"病态性"（导函数中同时含有较大参数和较小参数），本文提出了一种改进的Schur积多步法，数值实验表明，该方法能很好地抑制误差的急剧累积，与原方法相比，计算精度得到较大提高。

In order to achieve accurate solutions of ill-conditioned GPS equations with a few observational epochs, the ill-conditioned normal equations of GPS rapid positioning was transformed as a function optimization problem. Then genetic algorithm was used to calculate parameter solutions, which avoided the inversion of coefficient matrix of normal equations.

为准确解算仅有少数几个历元的GPS载波相位观测数据的病态定位方程，将GPS快速定位的病态法方程求解问题转化为一个函数优化问题，应用遗传算法求解病态方程，避免了法方程的求逆运算，从而可以得到参数的近似最优解。

To deal with data containing time drift, orthogonal polynomials fitting instead of least squares method is used.

研究了一种适用于这种过程的数据处理方法，利用权函数为1的特殊正交多项式做最佳平方逼近，从而避免求解病态方程组，得到较好的处理结果。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

Based on these, an improving μ-synthesis is presented, with which the high-purity distillation is designed well. 2. The robust performance problem of MIMO plant is explained with the plant direction angle, which shows that the robust performance varies with different input uncertainties and the μ-synthesis should be applied correctly according to the uncertainty structure. 3. Condition number and bandwidth are the important items for robust performance design in MIMO system. The H〓 two-block problems can not deal with the robust performance design of MIMO system because of the condition number cancellation. A general μ-synthesis procedure for MIMO system with uncertainties is presented. 4. For the SISO system, the object function in robust performance is amplified by at most 〓 than that of H〓 two-block problems in value: So the robust performance of SISO system can be done with the H〓 two-block problems to avoid the complicated μ-synthesis procedure. 5. All the conclusions and methods presented in this paper are demonstrated by some typical design examples.

从而形成一种改进的μ综合方去，并对精馏塔病态对象进行了鲁棒性能设计，得到令人满意的结果；（2）利用对象的方向角解释了MIMO对象鲁棒性能设计出现问题的原因，并提出不同输入摄动形式下系统的鲁棒性能问题也并不相同，因此利用μ综合处理鲁棒性能设计时，应根据不同的摄动情况采用不同的结构进行设计：（3）条件数问题和带宽问题是MIMO系统鲁棒性能设计的两个主要问题，指出由于条件数对消的存在使得一般H〓两块问题无法处理MIMO系统的鲁棒性能设计，而μ综合方法则是处理MIMO系统鲁棒性能设计的有效方法，并给出了其处理MIMO系统鲁棒性能设计的一般性方法；（4）提出对于SISO系统H〓两块问题（S/T问题、S/KS问题）的设计指标函数与鲁棒性能设计的μ指标函数在数值上最大差〓倍，因此对于一般SISO系统的鲁棒性能设计可以简单地用一般的H〓的两块问题处理，而避免μ综合设计的复杂过程；（5）本文中提出的结论和算法都利用H〓/μ发展中的典型例子：Doyle-Stein问题，Safonov的战斗机模型，精馏塔对象等进行了设计验证。

The process of convergence is to use the information of the time dimension. For the low signal noise ratio problem, detection of target in a single frame image is difficult, and the method is excellent.

考虑把点目标跟踪预测的过程视为是函数近似的过程，这是一个病态问题，可以用正则化理论来解决。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。