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...

Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE)-ba...

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...

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...