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the optimal approximations
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     The Optimal Approximations of Solutions to Singular Dirichlet Problems
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     Optimal temperature for D.
     各种光强下的暗呼吸速率均随温度升高而增大。
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  the optimal approximations
Donoho 7 studies the optimal approximations of particular classes of indicator functions with an overcomplete collection of atoms called wedgelets.
      


The minimax problem in mechanical design was usually solved with the optimal approximation theorem developed by Chebysbev. In a case where few design variables are available, however,correspondingly small number of limit deviation points should be selected, resulting in considerably longer time of calculation and lower approximating accuracy.It is shown by the method here proposed that the minimax problem can easily be formulated as a nonlinear programming with inequality parametric constraints when a...

The minimax problem in mechanical design was usually solved with the optimal approximation theorem developed by Chebysbev. In a case where few design variables are available, however,correspondingly small number of limit deviation points should be selected, resulting in considerably longer time of calculation and lower approximating accuracy.It is shown by the method here proposed that the minimax problem can easily be formulated as a nonlinear programming with inequality parametric constraints when a special variable and parametric constraints are used. An example of determining the balance weight for a mechanism and the optimal solution by SUMT are given.

机械设计中函数的极大值极小化问题,过去一般都是用契贝谢夫最佳逼近定理求解,但当设计变量少时,相应所取的极限偏差点不能多,因而逼近精度不高,且计算复杂.本文用非线性规划求解这类问题.理论分析和实际计算表明,只要引进带参数的约束条件及一个特殊变量,就可将这类问题转化为带不等式参数约束的非线性规划问题.文中还用这种新方法来确定机构的平衡重,并用SUMT外点法求出了最优解.

The relationship between the eigenvalues of both the large-scale system and its order-reduction model is derived from the requirement that their unit/impulse response matrices should be approximately equal to each other. With this formula, the time-domain optimal approximation for large-scale system simplification can be improved considerably, i.e. one needs only solve a parameter optimization problem instead of a functional problem. Two algorithms areproposed: 1, the optimal approximation...

The relationship between the eigenvalues of both the large-scale system and its order-reduction model is derived from the requirement that their unit/impulse response matrices should be approximately equal to each other. With this formula, the time-domain optimal approximation for large-scale system simplification can be improved considerably, i.e. one needs only solve a parameter optimization problem instead of a functional problem. Two algorithms areproposed: 1, the optimal approximation with the dominant eigenvalues retained; 2, the optimal approximation with some eigenvalues modified. A numerical example is also attached.

从大系统及其降阶模型的单位脉冲响应矩阵近似相等出发,推导了大系统及其降阶模型的特征值应该遵守的关系式。利用该关系式可以改进大系统模型简化的时域最优逼近法,将泛函求极值的问题转化为参数优化的问题,有可能使问题的解决简单化。本文提出了两种算法:1)保留主特征值的最优逼近;2)修改特征值的最优逼近。附有数字实例。

A problem of optimal approximation of matrix under spectral restriction has been put forward in the process of test and recovery of linear systems. In this paper we study the existence and uniqueness of the matrix A , which has the given eigenvalues and corresponding eigenvectors and is the optimal approximation of an observation matrix A obtained by the data of observation. Furthermore, a practical procedure is provided for computation.

在对一个线性系统进行观测或复原时,出于资料不全或对照资料进行核检等理由,曾提出过如下的数学问题: 根据对未知矩阵A的n~2个元素(?)_(ij)的观测(?)_(ij)以及理论或设计上对A的谱要求:A具有k个特征值λ_1,λ_2,……,λ_k及相应的特征向量X_1,X_2,……,X_k,如何对A作出某种意义下的最佳估计? 显然,据观测数据(?)_(ij)和先验的概率统计信息,可对A进行估计。设所得到的初步估计为(?)。但(?)未必能满足对A的谱要求,所以(?)未必是问题的解。因而我们考虑这样的一个问题:在所有满足谱约束的n阶方阵中,选取与(?)最“接近”的矩阵,以作为A的最佳估计。本文给出了A的最佳估计的存在性与唯一性,以及最佳估计的具体求法,最后用一个简单的算例来说明之。这里假定(?)已据现有的概率统计方法求得。

 
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