We analyze the impact of interior symmetries on the multiplicity of the eigenvalues of the Jacobian matrix at a fully synchronous equilibrium for the coupled cell systems associated to homogeneous networks. We consider also the special cases of regular and uniform networks. It follows from our results that the interior symmetries, as well as the reverse interior symmetries and quotient interior...

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, C. Padra, Appl. Numer. Math., 2012, for the approximation of Laplace eigenvalue problem with Crouzeix–Raviart non-conforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and ...

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way...

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of Jν(z); (B) the zeros of zJ ′ ν(z)...

A large literature has been devoted to the assessment of the right number of eigenvalues in PCA and CA (two-way and multiple). Most of the publications are based on distributional assuptions for the sample, or on bootstrap techniques. After having recalled some of the most important results, we present simple thresholds based on a « control chart » approach for eigenvalues as well as for contri...

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

Diversity analysis of a number of Multiple-Input Multiple-Output (MIMO) applications requires the calculation of the expectation of a function whose variables are the ordered multiple eigenvalues of a Wishart matrix. In order to carry out this calculation, we need the marginal pdf of an arbitrary subset of the ordered eigenvalues. In this letter, we derive an upper bound to the marginal pdf of ...

Quantum phase estimation is a cornerstone in quantum algorithm design, allowing for the inference of eigenvalues exponentially-large sparse matrices.The maximum rate at which these may be learned, --known as Heisenberg limit--, constrained by bounds on circuit complexity required to simulate an arbitrary Hamiltonian. Single-control qubit variants that do not require coherence between experiment...