Aggressive early deflation has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. One purpose of this paper is to point out that this deflation strategy is equivalent to extracting converged Ritz vectors from certain Krylov subspaces. As a special case, the single-shift QR algorithm enhanced with aggressive early deflation...

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh-Ritz method, is introduced. Asymptotic properties of ...

Mechanics of tympanic membrane (TM) is crucial for investigating the acoustic transmission through the ear. In this study, we studied the wrinkling behavior of tympanic membrane when it is exposed to mismatched air pressure between the ambient and the middle ear. The Rayleigh-Ritz method is adopted to analyze the critical wrinkling pressure and the fundamental eigenmode. An approximate analytic...

A new geometric invariant is defined from "first principles" for a point ensemble, which can represent clusters, molecules, crystals, and biomolecules. The scattering of a point ensemble is defined in terms of the Euclidean distance matrix and a vector measuring the weighted departure of the points from the cluster centre. Using the Rayleigh-Ritz theorem this function is maximized obtaining the...

Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a lowdimensional variational principle in the limit N → ∞ (where N is the number of types). In order to generalize these results, we consider here a large...

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential e...