In this article we further develop a perturbation approach to the Rayleigh– Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of the theory to nonnegative definite operators . The perturbation argument enables us to solve two problems in one go: We determine which part of the spectrum of the operator is being approximated by the Ritz values an...

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh-Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A = 3 and 4 nuclear systems. When the wave function of the system is expanded over a sufficiently large set of HH basis functions, containing or not correl...

A linear, aeroelastic analysis of a low aspect ratio swept back trapezoidal wing modeled as a cantilever plate is presented. An analytical and numerical formulation for both the aerodynamic forcing and structural response of the wing was developed. The analytical model uses a three dimensional time domain vortex lattice aerodynamic method. A Rayleigh-Ritz approach has been used to transfer equa...

An energy-based solution for calculating the buckling loads of partially anisotropic stiffened plates is presented, such as antisymmetric cross-ply and angle-ply laminations. A discrete approach, mathematical modelling formulations plates, followed. The developed extend Rayleigh–Ritz method explore available unstiffened plate solutions to interesting cases with some degree material anisotropy. ...

The Schrödinger equation for the 2S and 2P states of lithium-like ions Z = 5–7, 9–10 is solved by using Rayleigh-Ritz variational method in Hylleraas coordinates. leading-order relativistic QED corrections are calculated perturbatively higher-order estimated. transition frequencies between 1/2 J ( 1/2, 3/2) determined compared with experimental other theoretical results. Specifically, isotope s...

The aim of this paper is to provide a convergence analysis for a preconditioned subspace iteration, which is designated to determine a modest number of the smallest eigenvalues and its corresponding invariant subspace of eigenvectors of a large, symmetric positive definite matrix. The algorithm is built upon a subspace implementation of preconditioned inverse iteration, i.e., the well-known inv...

As Henri PoincarC once remarked, “solution of a mathematical problem” is a phrase of indefinite meaning. Pure mathematicians sometimes are satisfied with showing that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result as thc only reasonable goal. Such one sided views seem to reflect human limitations rather than objective values. I...