By the semi-inverse method, a variational principle is obtained for the Thomas– Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method. 2002 Elsevier Science Inc. All rights reserved.

This paper presents a novel approach for analyzing the free vibration response of variable-stiffness panels. A method is proposed herein, which relies upon combination R-functions and Ritz method. powerful peculiar aspect this consists in possibility handling any complex geometry with reduced modeling effort few degrees freedom to be handled. The so-obtained formulation particular interest earl...

Many inequality relations between real vector quantities can be succinctly expressed as “weak (sub)majorization” relations using the symbol ≺w. We explain these ideas and apply them in several areas: angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related. Let Θ(X ,Y) be the vector of principal angles in nondecreasing order between subspace...

The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix X with columns that form an orthonormal basis for a subspace X , and a Hermitian matrix A, the eigenvalues of XHAX are called Ritz values of A with respect to X . If the subspace X is A-invariant, then the Ritz values are some of the eigenvalues of A. If the A-invariant subspace X is perturbed to give rise to a...

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices...