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1.
Two elements enter the choice between 2 and 3SLS for full-system estimation: statistical efficiency and computational cost. 2SLS always has the computational edge, but 3SLS can be more efficient, a relative advantage that increases with the strength of the interrelations among the error terms. A measure of these interrelations is thus helpful in making the choice, and, when there are only two equations, this has suggested using a high pairwise error correlation as an indicator of when to use 3SLS. In larger systems of equations, however, these pairwise correlations can remain small even though more general interrelations give 3SLS the relative advantage. More general indicators are therefore needed, and this paper suggests three such and demonstrates their efficacy.Professor of Economics, Boston College, and Principal Research Associate, Center for Computational Research in Economics and Management Science, MIT. All computation was done on the TROLL system at MIT. My thanks go to Josh Charap for his able research assistance. This research was sponsored in part by the National Science Foundation under grant #IST-8420614. 相似文献
2.
A. Kaveh M. A. Sayarinejad 《International journal for numerical methods in engineering》2006,67(7):1012-1043
Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper‐symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper‐graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
3.
基于特征根比分布的协作频谱感知算法研究 总被引:1,自引:1,他引:0
介绍两种基于大维随机矩阵理论(Random Matrix Theory,RMT)的频谱感知方法,综合对比讨论并验证其感知性能。这些方法以采样协方差矩阵的最大最小特征根之比作为判决统计量与相应的判决门限相比较来确定频谱是否空闲。通过与能量检测(Energy Detection,ED)算法仿真对比,它们克服了能量检测中需要预知噪声信息的缺点,并具有不受噪声不确定度影响的优点,有较高检测性能和优越性。 相似文献
4.
Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which frequently results from applications with strong locality properties, a heuristic parallel algorithm is used to transform it into a block tridiagonal matrix such that the eigenvalue errors remain bounded by some prescribed accuracy tolerance. For a dense matrix without any usable structure, orthogonal transformations are used to reduce it to block tridiagonal form using mostly level 3 BLAS operations. Numerical experiments show that block tridiagonal structure obtained from this algorithm directly affects the computational complexity of the parallel block tridiagonal divide-and-conquer eigensolver. Reduction to block tridiagonal form provides significantly lower execution times, as well as memory traffic and communication cost, over the traditional reduction to tridiagonal form for eigensystem computations. 相似文献
5.
杨敏 《数字社区&智能家居》2010,(12)
给出了用Excel求实对称矩阵的全部特征值和特征向量的方法,该方法简单、直观,不需要设计程序,也不需要专门的数学软件,不仅为课堂教学,也为数值计算提供了方便。 相似文献
6.
7.
The necessary and sufficient conditions for global optimality are derived for an eigenvalue optimization problem. We consider
the generalized eigenvalue problem where real symmetric matrices on both sides are linear functions of design variables. In
this case, a minimization problem with eigenvalue constraints can be formulated as Semi-Definite Programming (SDP). From the
Karush-Kuhn-Tucker conditions of SDP, the necessary and sufficient conditions are derived for arbitrary multiplicity of the
lowest eigenvalues for the case where important lower bound constraints are considered for the design variables.
Received May 18, 2000 相似文献
8.
引入并讨论了对称箭头矩阵完成问题:在事先给定的对称箭头矩阵中嵌入一行一列使之成为新的对称箭头矩阵,并且具有指定最小最大特征值.利用箭头矩阵特征多项式之间的递归关系,给出并证明了这个问题存在惟一解的充要条件,以及解的一般公式与计算方法.同时还给出了存在非负解及均匀箭柄解的充要条件.利用该问题解决了逆特征值问题:求一个对称箭头矩阵,使它的各阶顺序主子阵具有给定的最小最大特征值.并给出该逆特征值问题解的计算方法.数值计算表明,该算法更有效. 相似文献
9.
《国际计算机数学杂志》2012,89(17):2410-2427
Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions. 相似文献
10.
《国际计算机数学杂志》2012,89(12):1849-1863
This paper presents a computational procedure for finding eigenvalues of a real matrix based on Alternate Quadrant Interlocking Factorization, a parallel direct method developed by Rao in 1994 for the solution of the general linear system Ax=b. The computational procedure is similar to LR algorithm as studied by Rutishauser in 1958 for finding eigenvalues of a general matrix. After a series of transformations the eigenvalues are obtained from simple 2×2 matrices derived from the main and cross diagonals of the limit matrix. A sufficient condition for the convergence of the computational procedure is proved. Numerical examples are given to demonstrate the method. 相似文献