it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil,the proposed algorithm reaches to convergence status.By using the deterministic discretetime(DDT)method,...
On an eigenvector-dependent nonlinear eigenvalue problem from the perspective of relative perturbation theory We are concerned with the eigenvector-dependent nonlinear eigenvalue problem (NEPv) H(V)V=VΛ, where H(V)∈n×n is a Hermitian matrix-valued function of V... NT A,RCL B - 《...
Eigenvector Distribution of Wigner Matrices We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a pr... A Knowles,J Yin - 《Probability Theory & Related Fields》 被引量: 151发表: 2011年 ...
An iterative procedure is proposed for computing the eigenvalues and eigenvectors of Hermitian Toeplitz matrices. The computational cost per eigenvalue-eig... FW Trench - 《Siam Journal on Matrix Analysis & Applications》 被引量: 147发表: 1989年 A new approach to electrochemical simulations based on...
Triangular factorization of structured Hermitian matrices I. Gohberg (Ed.), Operator Theory: Advances and Applications, vol. 18, Birkhäuser, Boston, MA (1986), pp. 301-324 CrossrefGoogle Scholar [50] M. Mansour Stability criteria of linear systems and the second method of Lyapunov Sientia ...
As for Hermitian matrices, the key point is to prove the existence of at least one nonzero eigenvector. 对于埃尔米特矩阵,关键在于存在至少一个非零向量。 LASER-wikipedia2 The smallest eigenvalue for every Laplacian matrix is 0, and its corresponding eigenvector is [1, 1, . . . , 1]...
Our proposed method applies to nonsquare matrices, complex hermitian matrices and also to infinite dimensional cases such as self-adjoint elliptic operators, some of which will be presented as specific applications. 展开 年份: 2016 收藏 引用 批量引用 报错 分享 ...
I'm working on a project in which we would like to compute gradients for a function that depends on eigenvalues of non-hermitian matrices (but not eigenvectors). From what I understand, the difficulty lies in computing gradients for the eigenvectors of eig due to ambiguity in the phase. Woul...
The former aredef i ned as satisfying the condition H = H † ≡¯H T , with†standing for Hermitian conjugation,Tdenoting thetranspose of the matrix and the bar standing for the complex conjugation of its entries. All Hermitian matricesare by def i nition normal, with vanishing ...
A∗, AT, AH, and A† denote the conjugate, transpose, Hermitian transpose, and pseudo inverse of A, respectively. We will use ⊗ for the Kronecker product, ⊙ for the Khatri-Rao (columnwise Kronecker) product [23], I n for a n×n identify matrix, 0m×n for an m×n zero ...