This paper is concerned with the Hermitian definite generalized eigenvalue problem A - 位B for block diagonal matrices A 1/4 diagA11; A22 and B 1/4 diagB11; B22. Both A and B are Hermitian, and B is positive definite. Bounds on how its eigenvalues vary when A and B are perturbed ...
Example 5.5.2 Block-Diagonal Matrix Find the eigenvalues and eigenvectors of (5.22)H=010100002.Writing the secular equation and expanding in minors using the third row, we have (5.23)-λ101-λ0002-λ=(2-λ)-λ11-λ=(2-λ)(λ2-1)=0.We see that the eigenvalues are 2, +1, and -...
PERTURBATION OF PARTITIONED HERMITIAN DEFINITE GENERALIZED EIGENVALUE PROBLEMS * REN-CANG LI † , YUJI NAKATSUKASA ‡ , NINOSLAV TRUHAR § , AND SHUFANG XU ¶ Abstract. This paper is concerned with the Hermitian definite generalized eigenvalue problem A−λB for block diagonal matrices A ...
We are not aware of such a result in the literature, but will see that the claim is at least true for $3 imes 3$ matrices. In this paper, we suggest to extend the above model by considering matrices which differ from isospectral ones only by multiplication with a block diagonal matrix ...
18.Equivalent Representation of Block α-Diagonally Dominant Matrix and Its applications块α-对角占优矩阵的等价表征及应用 相关短句/例句 Dominant eigenvalue占优本征值 1.Using the method of functional analysis,especially the linear operator theory on Banach space,the existence of the strictly dominant ...
The class of perturbation considered is wide and ignores only the phase information of the individual elements of the perturbation matrix; it encompasses diagonal, block-diagonal and other forms of block-structured perturbations. The techniques developed provide a means of assessing stability margins and...
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonaliz... Mostafazadeh,Ali - 《Journal of Mathematical Physics》 被引量: 124发表: 2002年 Spectral bundle methods for non-convex maximum eigenvalue funct...
- 《Siam Journal on Matrix Analysis & Applications》 被引量: 7发表: 2015年 EIGENVALUE PROBLEM This paper is concerned with the Hermitian definite generalized eigenvalue problem A - 位B for block diagonal matrices A 1/4 diagA11; A22 and B 1/4 diagB11... Jingbo Dou,Pengcheng Niu,Zixia ...
Teuchos::ArrayRCP<SC> diag = Utils::GetMatrixDiagonal(*A); Utils::MyOldScaleMatrix(AP, diag,true, doFillComplete, optimizeStorage);//scale matrix with reciprocal of diag} Scalar lambdaMax; {SubFactoryMonitorm2(*this,"Eigenvalue estimate", coarseLevel); ...
The purpose of this paper is to generalize (5) by including the off-diagonal blocks K and ⁎K⁎. The main results are the following majorization inequalities. Denote i=−1. Theorem 1 Let ⁎H=(MKK⁎N) be a positive semidefinite block matrix with square matrices M and N of the ...