In this paper we apply a minmax characterization for nonoverdamped nonlinear eigenvalue problems to a rational eigenproblem governing mechanical vibrations of a tube bundle immersed in an inviscid compressible fluid. This eigenproblem is nonstandard in two respects: it depends rationally on the eigenparameter, and it involves non-local boundary conditions. Comparison results are proved comparin...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

for all complex vectors ai and bj . One can easily prove that if X is positive definite then X is hermitian (see, e.g., Ref. [1], p. 65). Since the eigenvalues of hermitian matrices are real, it is easy to prove that the eigenvalues of positive definite matrices are real and positive. Moreover, a positive definite matrix is invertible, since it does not possess a zero eigenvalue. Note that a no...

Most commonly used face recognition algorithms are based on extraction of global features using eigenvalue decomposition of some relational matrix of image intensity values. Real time face recognition applications require a computationally efficient algorithm for eigenvalues generation. Fast principal component analysis (FPCA) is an algorithm for efficient generation of eigenvalues which improv...

The slow convergence of the Incomplete Cholesky preconditioned Conjugate Gradient (CG) method, applied to solve the system representing a magnetostatic finite element model, is caused by the presence of a few little eigenvalues in the spectrum of the system matrix. The corresponding eigenvectors reflect large relative differences in permeability. A significant convergence improvement is achieve...

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least k column vectors, where k is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show t...

Eigensolvers involving complex moments can determine all the eigenvalues in a given region plane and corresponding eigenvectors of regular linear matrix pencil. The moment acts as filter for extracting eigencomponents interest from random vectors or matrices. This study extends projection method eigenproblems to singular nonsquare case, thus replacing standard inverse resolvent with pseudoinver...

Given two vectors a; 2 Rn, the Schur-Horn theorem states that a majorizes if and only if there exists a Hermitian matrix H with eigenvalues and diagonal entries a. While the theory is regarded as classical by now, the known proof is not constructive. To construct a Hermitian matrix from its diagonal entries and eigenvalues therefore becomes an interesting and challenging inverse eigenvalue prob...

We propose a simple algorithm for improving the MDL (minimum description length) estimator of the number of sources of signals impinging on multiple sensors. The algorithm is based on the norms of vectors whose elements are the normalized and nonlinearly scaled eigenvalues of the received signal covariance matrix and the corresponding normalized indexes. Such norms are used to discriminate the ...