Using QR-like decomposition with column pivoting and least squares techniques, we propose a new and ecient algorithm for solving symmetric generalized inverse eigenvalue problems, and give its locally quadratic convergence analysis. We also present some numerical experiments which illustrate the behaviour of our algorithm. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65...

We propose two semismooth Newton methods for seeking the eigenvalues of a linear transformation relative to Lorentz cones, by the natural equation reformulation and the normal equation reformulation, respectively, and establish their local quadratic convergence results under suitable conditions. The convergence analysis shows that the method based on the natural equation formulation is not infl...

In this paper we examine a spatially two–dimensional forced, damped Boussinesq equation with quadratic nonlinearity. This equation describes small, nonlinear oscillations of a circular, elastic membrane in the presence of viscosity. The eigenfunction expansion method is used for the purpose of constructing solutions for small initial data analytically. The constructive method enables us to perf...

We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of λ1, the smallest eigenvalue of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes th...

One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: here the shift s is the eigenvalue of the bottom 2 × 2 principal minor closest to the corner entry. It has been a long-standing conjecture that the rate of convergence of the algorithm is cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly qu...