正定

词组短语

positive definite

与正定相关的网络例句 [注：此内容来源于网络，仅供参考]

It consists of the next three aspects: firstly, we study Murthys' open problem whether the augmented matrix is a Q0-matrix for an arbitary square matrix A , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the Graves algorithm can be used to solve linear complementarity problem with bisymmetry Po-matrices; Secondly, we study Murthys' conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study Pang's conjecture , obtain two conditions when R0-matrices and Q-matrices are equivelent and some properties about E0 ∩ Q-matrices; Lastly, we give a counterexample to prove Danao's conjecture that if A is a Po-matrix, A ∈ E' A ∈ P1* is false, point out some mistakes of Murthys in [20] , obtain when n = 2 or 3, A ∈ E' A ∈ P1*, i.e.

本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想：(1)研究了Murthy等在[2]中提出的公开问题，即对任意的矩阵A，其扩充矩阵是否为Q_0-矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了Graves算法，证明了若A是双对称的P_0-矩阵时，LCP可由Graves算法给出；(2)研究了Murthy等在[6]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了Pang~-猜想，得到了只R_0-矩阵与Q-矩阵的二个等价条件，以及E_0∩Q-矩阵的一些性质；(3)研究了Danao在[25]中提出的Danao猜想，即，若A为P_0-矩阵，则，我们给出了反例证明了此猜想当n≥4时不成立，指出了Murthy等在[20]中的一些错误，得到n=2，3时，即[25]中定理3.2中A∈P_0的条件可以去掉。

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 thesis has mainly contributed two results in theory: one is that the covariance matrix is not positive definitive if the number of sampling is least than the number of variables, the other is that the covariance matrix of discrete sample is positive definitive if and only if the sum of every random column vector of data matrix is non I-linear combination.

本论文在理论上，主要得出两个新的结果：ⅰ抽样调查中，若样本的个数少于变量的个数则样本协方差矩阵恒为非正定；ⅱ离散型样本协方差矩阵正定的充要条件是样本资料阵的各随机列向量是非I-线性组合。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

In a special case of 2 dimensional variables, the probability of the positive definitiveness of the discrete sample covariance matrix is given in term of sample size and variable dimension. Based on the results, the optimal sample size is provided in this thesis.

推出了离散型样本协方差矩阵正定的充要条件，得到了求离散型样本协方差矩阵正定概率的模型，建立了特殊情况下的抽样优化模型。

It is a natural generalization of the notion of implicative ideals in BCK algebras.

证明了BCI代数的一个非空子集是BCI关联理想当且仅当它既是BCI交换理想又是BCI正定关联理想，从而揭示了这三类理想之间的内在联系，并将BCK代数中知名论断：BCK代数的一个非空子集是关联理想当且仅当它既是交换理想又是正定关联理想，推广到BCI代数上去。

This paper will put the concept of definiting generalized positive definite matrices in Paper[1, 4] into the further extensions, discuss the inclusion relation betweenness generalized positive definite matrices in all the different definitions, and give four new definitions on an equality with M-Matrices.

摘要将文[1，4]中定义广义正定矩阵的概念再作推广，并讨论各种不同定义下的广义正定矩阵间的包含关系，给出M-矩阵等价的四种新定义。

The first way is to ensure the kernel function to be positive definite by introducing space mapping transformation;the second way is using similar-SVR model to solve the unsolvable problem of SVR model with non-positive definite kernel function.

一是通过引入空间映射变换保证所得到的SVR的核函数是正定的；二是利用近似SVR模型解决具有非正定核的SVR模型的不可解问题。

The text for making every variety positive definite matrix and positive sub-definite matrix to unification, the concept of almost positive definite matrix is given, and its properties and determinant theories are discussed, and many new results are obtained.

本文研究了各类正定矩阵与次正定矩阵的基本性质及行列式理论，提出了准正定矩阵的概念，获得了许多新的结果，推广了Hadamard、Openheim、Ostrowski-Taussky与Minkowski等著名不等式以及屠伯埙、杨新民等的有关结果，扩大了Minkowski不等式的指数范围。

Not every partial positive definite Toeplitz matrix has Toeplitz positive definite completion and not every par2 tial positive definite matrix which has positive definite completion has Toeplitz positive definite completion.

并不是所有的部分正定Toeplitz 矩阵都有Toeplitz 正定完成，也并不是每个有正定完成的部分正定矩阵都有 Toeplitz 正定完成。

与正定相关的网络解释 [注：此内容来源于网络，仅供参考]

positive definite：正定,正定的

positive damping 正阻尼 | positive definite 正定,正定的 | positive definite differential form of degree two 正定二次微分形式

positive definite Hermitian form：正定埃尔米特型

positive definite function 正定関数 | positive definite Hermitian form 正定埃尔米特型 | positive definite Hermitian inner product 正定埃尔米特内积

positive definite Hermitian matrix：正定埃尔米特矩阵

positive definite Hermitian inner product 正定埃尔米特内积 | positive definite Hermitian matrix 正定埃尔米特矩阵 | positive definite Hermitian operator 正定埃尔米特算子

positive definite Hermitian operator：正定埃尔米特算子

positive definite Hermitian matrix 正定埃尔米特矩阵 | positive definite Hermitian operator 正定埃尔米特算子 | positive definite Hermitian transformation 正定埃尔米特变换

positive definite Hermitian transformation：正定埃尔米特变换

positive definite Hermitian operator 正定埃尔米特算子 | positive definite Hermitian transformation 正定埃尔米特变换 | positive definite inner product 正定内积

positive definite quatratic form：正定二次型

positive definite matrix 正定矩阵 | positive definite quatratic form 正定二次型 | positive semidefinite matrix 半正定矩阵

positive definite differential form of degree two：正定二次微分形式

positive definite 正定,正定的 | positive definite differential form of degree two 正定二次微分形式 | positive definite form 正定型

positive definite symmetric kernel：正定对称核

positive definite sequence 正定序列 | positive definite symmetric kernel 正定对称核 | positive definite symmetric matrices 正定对称矩阵

positive definite matrix：正定方阵

正定核 positive definite kernel | 正定方阵 positive definite matrix | 正定算子 positive definite operator

positive definite matrix：正定行列

positive definite kernel 正定核 | positive definite matrix 正定行列 | positive definite operator 正定算子