Quadratic eigenvalue problems (QEPs) appear in almost all vibration analysis of systems, such as buildings, circuits, acoustic structures, and so on. Conventional numerical method for QEPs is to linearize a QEP as a doublly-sized generalized eigenvalue problem (GEP), then call a backward stable algorithm to solve the GEP, for example, the QZ for dense GEP, and at last recover approximated eigen...

In this paper we concern the inverse problem of constructing the n-by-n real symmetric tridiagonal matrices C and K so that the monic quadratic pencil Q(λ) := λI + λC + K (where I is the identity matrix) possesses the given partial eigendata. We first provide the sufficient and necessary conditions for the existence of an exact solution to the inverse problem from the self-conjugate set of pres...

Let A = " M R R N # and ~ A = " M 0 0 N # be Hermitian matrices. Stronger and more general O(kRk 2) bounds relating the eigen-values of A and ~ A are proved using a Schur complement technique. These results extend to singular values and to eigenvalues of non-Hermitian matrices. (1) be Hermitian matrices. Since jjA ? ~ Ajj = jjRjj one can bound the diierence between their eigenvalues in terms of...

In this work we present a new method to compute the delays of delay differential equations (DDEs), such that the DDE has a purely imaginary eigenvalue. For delay differential equations with multiple delays, the critical curves or critical surfaces in delay space (that is, the set of delays where the DDE has a purely imaginary eigenvalue) are parameterized. We show how the method is related to o...

We examine the variance of a linear statistic defined on symmetric group endowed with Ewens probability. Despite dependence summands, it can be bounded from above by constant multiple sum variances summands. find exact value this constant. The analysis appearing quadratic forms and eigenvalue search is built upon exponential matrices discrete Hahn’s polynomials.

The convex hull relaxation (CHR) method (Albornoz 1998, Ahlatçıoğlu 2007, Ahlatçıoğlu and Guignard 2010) provides lower bounds and feasible solutions on convex 0-1 nonlinear programming problems with linear constraints. In the quadratic case, these bounds may often be improved by a preprocessing step that adds to the quadratic objective function terms that are equal to 0 for all 0-1 feasible so...