Multidimensional stability problems lead to huge eigenvalue problems of the type Ax equals lambda Bx, which are only solvable when the matrix structures are not touched. In this package, A and B have block diagonal form. The inverse vector iteration is used which converges towards the lowest ...
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 ...
To overcome difficulties arising in the presence of infinite eigenvalues with high-order Jordan block, we introduce a new procedure which could be used as "preprocessing" to deflate the infinite eigenvalue. This method initially reduces B to a diagonal matrix with nonnegative entries and deflates ...
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...
Block-floating vectors and matrices 119 Fundamental limitations of 2-digit computation 120 Eigenvalue techniques based on reduction by similarity transformations 123 Error analysis of methods based on elementary non-unitary trans- formations 124 Error analysis of methods based on elementary unitary ...
The matrix\(\varvec{S}\varvec{A}\)is symmetric because\(\varvec{C}\)and\(M_j\), for\(j \ge 0\), are symmetric. By using (11a) we get that the first block-row of\(\varvec{S}\varvec{B}\)is equal to its first block column, whereas the equation (11b) and the symmetry...
state. Whitlock and Barton (1997) showed that these linear recursions are closely related. They also argued briefly that the transition matrix of the Markov chain of allele frequencies has its largest non-unit eigenvalue equal to, and therefore all effective sizes of the previous paragraph agree...
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 ...
Σ is a m × n matrix, with the top left n × n block in diagonal form with σi ’s on the diagonal and the bottom (m ? n) × n rows zero. Without loss of any generality, we let σ1 ≥σ2 ≥···σn≥ 0. These σi ’s are called the singular values of A (or AH...
If so then the adjacency matrix has two off-diagonal blocks, say H and HT (diagonal blocks are zero matrices), so that the matrix H which is a block in the first row and second column of A has a step-wise form (see Fig. 2.1). This canonical matrix can be also used for defining...