Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review...Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).展开更多
针对最大最小特征值检测法(Maximum-minimum Eigenvalues Based Detector,MMED)需要对协方差矩阵进行特征分解,计算复杂度较高的问题,提出了一种基于采样协方差矩阵行列式的频谱感知方法。该频谱感知方法利用了矩阵行列式的所有特征值,...针对最大最小特征值检测法(Maximum-minimum Eigenvalues Based Detector,MMED)需要对协方差矩阵进行特征分解,计算复杂度较高的问题,提出了一种基于采样协方差矩阵行列式的频谱感知方法。该频谱感知方法利用了矩阵行列式的所有特征值,只需要计算采样协方差矩阵的行列式,即可得到接近或者稍优于MMED的感知结果。仿真分析结果表明,与MMED相比,所提出的频谱感知方法不仅计算复杂度低,而且具有更佳的感知性能。展开更多
图示评审技术(graphic evaluation and review technique,GERT)解析法一般利用信号流图的拓扑特征(梅森公式)和矩母函数进行求解,但当GERT网络节点较多且结构复杂(回路众多)时,拓扑结构特征的分析十分困难,易出现错判或遗漏情况。针对...图示评审技术(graphic evaluation and review technique,GERT)解析法一般利用信号流图的拓扑特征(梅森公式)和矩母函数进行求解,但当GERT网络节点较多且结构复杂(回路众多)时,拓扑结构特征的分析十分困难,易出现错判或遗漏情况。针对此问题,将GERT网络用矩阵形式进行表征,分析了以梅森公式为基础的解析法与矩阵变换的关系,设计了两类基于矩阵的GERT求解算法。首先给出GERT网络与信号流图增益矩阵、流图增益矩阵一一对应关系,分析增益矩阵行列式变换与信号流图求解公式的对应关系,设计GERT网络的增益矩阵行列式变换求解算法。另外,研究GERT网络(信号流图)化简操作(消除自环、消除节点)在信号流图增益矩阵上的变换形式,提出了GERT网络解析的矩阵变换方法。最后用两个例子说明矩阵表征及求解模型的简便性和正确性,为GERT解析的计算机操作奠定基础。展开更多
In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterat...In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterative processes, are obtained.展开更多
文摘Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).
文摘针对最大最小特征值检测法(Maximum-minimum Eigenvalues Based Detector,MMED)需要对协方差矩阵进行特征分解,计算复杂度较高的问题,提出了一种基于采样协方差矩阵行列式的频谱感知方法。该频谱感知方法利用了矩阵行列式的所有特征值,只需要计算采样协方差矩阵的行列式,即可得到接近或者稍优于MMED的感知结果。仿真分析结果表明,与MMED相比,所提出的频谱感知方法不仅计算复杂度低,而且具有更佳的感知性能。
文摘图示评审技术(graphic evaluation and review technique,GERT)解析法一般利用信号流图的拓扑特征(梅森公式)和矩母函数进行求解,但当GERT网络节点较多且结构复杂(回路众多)时,拓扑结构特征的分析十分困难,易出现错判或遗漏情况。针对此问题,将GERT网络用矩阵形式进行表征,分析了以梅森公式为基础的解析法与矩阵变换的关系,设计了两类基于矩阵的GERT求解算法。首先给出GERT网络与信号流图增益矩阵、流图增益矩阵一一对应关系,分析增益矩阵行列式变换与信号流图求解公式的对应关系,设计GERT网络的增益矩阵行列式变换求解算法。另外,研究GERT网络(信号流图)化简操作(消除自环、消除节点)在信号流图增益矩阵上的变换形式,提出了GERT网络解析的矩阵变换方法。最后用两个例子说明矩阵表征及求解模型的简便性和正确性,为GERT解析的计算机操作奠定基础。
文摘In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterative processes, are obtained.
