特征值

基本解释 (translations)

eigenvalue

词组短语

characteristic value · proper value

与特征值相关的网络例句 [注：此内容来源于网络，仅供参考]

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

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

We then diagonalize the matrix C and obtain the eigenvalue spectrum and eigenvectors. The large eigenvalues which go beyond the upper bound of the random matrix, i.e., the Wishart matrix, reflect the local correlations between stocks. The largest eigenvalue corresponds to the market mode, and next large eigenvalues represent the interactions between stocks in a same sector.

进一步，通过对角化，我们得到矩阵C的特征值谱和特征向量，超过随机的Wishart矩阵特征值谱上边界的特征值反映了股票间的局域关联，其中最大的特征值对应于市场模式，其余的次大特征值代表了同一板块内股票间的相互作用。

First scanning the known handwriting materials then number them ,In pretreatment, we convert the valid part of the image into a standard size, as images carries out duotone and go throw off chirp handling in order to achieve better effect.draw features from the known handwriting materials with the Co-occurence,especially,we divided a copy of handwriting into 25 little pieces with the size of 128*128 ,drawing features from every little piecese with four directions(0 degree, 45 degrees, 90 degrees as well as 135 degrees) and calculate the four major feature values( veins and the statistical quantity of veins contrast and the statistical quantity of veins consistency Shang the statistical quantity of statistical quantity as well as the veins correlation of gray scale ), preservation all the feature value that drawn from all known ma terials to the handwriting characteristic database,then input the unknown handwriting materials, also using the method of the Co-occurence to draw those features, recycling the minimum European Distance law match the unknown writing material feature value with the handwriting characteristic feature database, export the label of the known hand writing materials which is most similar to the unknown material with minimum European Distance, and then we can confirm who is the author of the unknown material.

首先将笔迹材料作为图象扫描输入，并对其进行编号。预处理部分可将笔迹图象的有效部分规范化到一个统一尺寸，接着对其进行二值化和去除噪声的处理，以便于更好的提取图像的特征。在此我们采用了灰度共生矩阵法提取手写笔迹材料的纹理特征，与以往有所不同的是，我们将一份手写材料分割成64块大小为80*80象素的子图象，每个小块都从四个方向（0度、45度、90度以及135度）来更全面的提取特征，并计算出四个最主要的特征值（纹理一致性的统计量、纹理反差的统计量、纹理熵的统计量以及纹理灰度相关性的统计量），将从所有已知材料提取的特征值保存到纹理特征库中，对于待检手写材料，同样采用灰度共生矩阵的方法提取其纹理特征，再利用最小欧氏距离分类法将从待检手写材料中提取的特征值与纹理特征库中的特征值进行比对，与欧氏距离比对值最小的相匹配，输出匹配成功的原材料的标号，进而识别出待检材料书写者的身份。

Therefore, in order to offer reference to Readers, based on idempotent matrix, involutory matrix, nilpotent matrix, diagonal matrix, the main character of special matrix are proved in this paper after the Defined and algorithm of eigenvalue of matrix .for example , some problems of the eigenvalues of matrix are solved in a special method based on the eigenvalues of matrix .

为此， 本文除了介绍矩阵特征值的定义和算法外，还围绕幂等矩阵、幂零矩阵、对角矩阵、等特殊矩阵给出了其主要性质并加以证明，同时还介绍了一些特殊矩阵的特征值的算法，例如：本文利用矩阵的特征值，对与矩阵的特征值相关的一些典型问题给出了较好的处理方法。

And the sufficient and necessary conditions are obtained and the uniqueness of T is discussed and an algorithm for solving the inverse problem is provided. The other kind of structure inverse eigenvalue problem is for unitary Hessenberg matrices with positive subdiagonal elements. That is, a unitary Hessenberg matrices with positive sub-diagonal elements can be constructed when its eigenvalues and the eigenvalues of H_(11) and H_(22) are known. Here H_(11) and H_(22) are rank-one modifications of k × k leading principal submatrix of H and of its × remain submatrix respectively. In the end, the uniqueness of H and an algorithm is obtained.

文中首先讨论了这三组特征值之间的交错关系，接着确定了该逆问题有解的充要条件，并论证了其解的唯一性问题，最后给出了相应的数值算法；本文第二个问题解决的是一类不可约的酉Hessenberg阵的逆特征值问题：即一个不可约的酉Hessenberg阵可以由它的特征值、它的前k阶秩一修正的顺序主子阵的特征值以及它的后n—k阶余子阵的秩一修正阵的特征值来确定，文中最后讨论了唯一性和相应的算法。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

Firstly, an inverse eigenvalue problem for Jacobi matrices is presented: we could construct the Jacobi matrix T if we know the spectral data: the eigenvalues of T and the eigenvalues of T_1 and of T_2, where T_1 is different to the k × k leading principal submatrix of T only at the position, while T_2 is different to the × remain submatrix only at the (1, 1) position.

首先给出的是一类Jacobi阵的逆特征值问题，即给定三组实数：一组是Jacobi阵的n个特征值，一组是只修改了最后一个对角元的它的前k阶顺序主子阵的特征值，最后一组是修改了第一个对角元的后n—k阶余子阵的特征值，用这些给定的特征值来确定相应的Jacobi矩阵。

The perturbational reanalysis method of repeated eigenvalues and associated eigenvectors of the lineargeneralized eigenvalue problem is further investigated on the basis of the relevant results of previous stud-ies.

本文基于已有研究结果，进一步探讨了线性广义特征值问题的重特征值及其特征向量摄动重分析理论和方法，阐述了重特征值情形下摄动重分析方法的一些重要特点，完善了重特征值的特征向量的二阶摄动算式，并论证了重特征值摄动法与相异特征值摄动法之间的统一性。

Following from the results of sensitivity analysis of standard eigenvalue problems,the differentiability of semisimple multiple eigenvalues of nonsymmetric generalized eigenvalue problems is proved,and the derivatives of semisimple multiple eigenvalues and the series expansions of the corresponding eigenvectors are obtained.

以标准特征值问题灵敏度分析的有关结论为基础，证明了单参数非对称广义特征值问题半单重特征值的可微性，给出了特征值导数的表达式和特征向量的级数展开式。以所得结论为基础，定义了广义特征值问题半单重特征值的灵敏度，给出了确定矩阵对中敏感元素的方法

与特征值相关的网络解释 [注：此内容来源于网络，仅供参考]

characteristic value matrix：特征值表

characteristic value inheritance 特征值继承 | characteristic value matrix 特征值表 | characteristic value record 特征值记录

characteristic value：特征值

characteristic point 特性点 | characteristic value 特征值 | characteristics 特征

characteristic value assignment：特征值分配

characteristic value assignment screen 特征值指定屏幕 | characteristic value assignment 特征值分配 | characteristic value check 特征值检查

characteristic value inheritance：特征值继承

characteristic value description 特征值描述 | characteristic value inheritance 特征值继承 | characteristic value matrix 特征值表

characteristic value description：特征值描述

characteristic value dependency 特征值依赖 | characteristic value description 特征值描述 | characteristic value inheritance 特征值继承

eigenvalue problem：特征值问题

最优特征值:dominance eigenvalue | 特征值问题:eigenvalue problem | 逆特征值:Inverse eigenvalue

eigenvalue problem：特征值间题

特征值校正:eigenvalue correction | 特征值间题:eigenvalue problem | 特征值法:the eigenvalue method

generalized inverse characterize value problems of matrices：广义逆特征值问题

矩阵广义逆特征值问题:generalized inverse eigenvalue problems... | 广义逆特征值问题:generalized inverse characterize value problems of matrices | 抽象广义矢量平衡问题:Abstract generalized vector equilib...

proper value of matrix：方阵的特征值(固有值)

特征值;固有值 proper value | 方阵的特征值(固有值) proper value of matrix | 特征(固有)向量 proper vector

eigenvalues：计算矩阵的特征值

EigenConditionNumbers 计算数值特征值制约问题的特征值或特征向量的条件数 | Eigenvalues 计算矩阵的特征值 | Eigenvectors 计算矩阵的特征向量