We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iterat...

A gradient projection method with feasible inexact projections is proposed in the present paper. The performed using a general relative error tolerance. Asymptotic convergence analysis under quasiconvexity assumption and iteration-complexity bounds convexity of employing constant Armijo step sizes are presented. Numerical results reported illustrating potential advantages considering instead ex...

Abstract. We present a detailed convergence analysis of preconditioned MINRES for approximately solving the linear systems that arise when Rayleigh Quotient Iteration is used to compute the lowest eigenpair of a symmetric positive definite matrix. We provide insight into the “slow start” of MINRES iteration in both a qualitative and quantitative way, and show that the convergence of MINRES main...

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the...

A Ulm-like method is proposed in [13] for solving inverse eigenvalue problems with distinct given eigenvalues. The Ulm-like method avoids solving the Jacobian equations used in Newton-like methods and is shown to be quadratically convergent in the root sense. However, the numerical experiments in [3] only show that the Ulm-like method is comparable to the inexact Newton-like method. In this sho...