正定矩阵

In this paper, an extended divide and conquer algorithm is intended proposed, which is for solving the real symmetric band generalized eigenvalue problem under distributing environment Eigenvalue partition theorem is presented and proved Based on divide and conquer by extension, this algorithm computes generalized eigenpaires of symmetric band matrix pencil by bisection and generalized Rayleigh quotient iteration Theoretic analysis and numerical results show that this algorithm is better than the classic software package LAPACK when bandwidth is small and the scale is large Combined with multisection, which has good parallelism, it got good effects under distributed environments

提出了分布式环境下计算对称带状广义特征值问题的一种扩展分治算法，给出了特征值分割定理及其证明算法在扩展分治的基础上，利用二分压缩结合广义Rayleigh商迭代计算广义特征对理论分析和数值实验表明，对于窄带宽大规模的广义特征值问题，该分治算法明显优于LAPACK软件包结合并行性好的多分法，在分布式环境下获得了很好的并行效果1 引言本文研究了对称带状广义特征值问题Ax =λBx ( 1)的并行计算，其中，A ，B均为半带宽为r的n阶实对称带状矩阵且其中之一是正定的本文总假设B是正定的求解此问题有两种传统方法，第1种方法是通过计算矩阵B的Cholesky分解，将问题( 1)转化为标准特征值问题[1～3] ，进一步

This condition only requires finding a common positive-definite matrix in each maximal overlapped-rule group. It can reduce the difficulty of former stability analysis approaches.

该条件只需在各最大交叠规则组内分别寻找公共的正定矩阵，减小了以往稳定性判定方法的局限性和难度。

It wishes to find a new way for normative research into the concept of generalized positive definite matrix.

希望为广义正定矩阵概念的规范化探出一条新路。

However, a great lot of fuzzy rules are needed to approximate a complex nonlinear system, which can lead to a great lot of LMIs related to the number of fuzzy rules. In this case, positive definite matrix P might not exist.

可是，当需要大量的模糊规则来逼近一个复杂的非线性系统时，就导出与模糊规则数有关的大量LMIs，这可能会导致正定矩阵P不存在。

But also extend and improve the recent literature on the lower bound estimate of the determinant modulo about the Hadamard product of the complex generalized positive definite matrix.

而且也推广和改进了最近有关复广义正定矩阵的Hadamard乘积的行列式的模的下界估计文献。

Lastly,two sorts of splitting of definite positive matrix areformed,one of which is combined with U-transformation to put forward aniteration process for the sort of periodic structures.

构造了正定矩阵的两种分解格式，由此对于一类周期结构提出了一种酉变换迭代算法。

The relevant research results of the general positive definte matrix are generalized and improved.

推广和改进了近期广义正定矩阵的一些相关研究结果。

A criterion for the real part positive semidefiniteness matrix is presented,and the algorithm for this criterion is given.

给出了实部半正定矩阵的一种判定方法，并给出了该判定方法的算法。

The properties and determinant theories of the almost positive subdefinite matrix and determi- nant are discussed.

研究准次正定矩阵的性质及行列式理论。

Stage multisplitting symmetric positive semidefinite matrices is obtained.

较深入地讨论了对称半正定矩阵的二级多分裂方法。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷