This paper presents a new dual-band elliptical dielectric resonator antenna (EDRA). The EDRA is mounted on a ground plane and fed with a rectangular slot exited by a microstrip line. By optimizing the structure parameters, it is possible to obtain more than one excited mode in a limited frequency band. Numerical and measurement results for the radiation patterns of this slot fed EDRA are given ...

The FEAST algorithm [5] is an algorithm aimed at solving generalized eigenvalue problems AX = BXΛ, where A,B are n×n matrices. In [4] we presented a short analysis of FEAST involving this eigenvalue problem. In the present work we focus on the real symmetric eigenvalue problem AX = XΛ, where A = A, XX = I and Λ is a diagonal matrix consisting of real eigenvalues. These eigenvalues are sought in...

In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green’s functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl’s m-functio...

A fast current pulse causes a material to heat and undergo rapid expansion. We calculate the response of a cylindrically shaped material to a pulse on the microsecond time scale. The first step is to obtain the breathing modes of elastic oscillation of the cylinder. These modes are calculated using a Rayleigh–Ritz variational method introduced by Demarest for cubes. The boundary conditions are ...

The topic of this paper is the convergence analysis of subspace gradient iterations for the simultaneous computation of a few of the smallest eigenvalues plus eigenvectors of a symmetric and positive definite matrix pair (A,M). The methods are based on subspace iterations for A−1M and use the Rayleigh-Ritz procedure for convergence acceleration. New sharp convergence estimates are proved by gen...

The Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR method) finds the eigenvalues in a certain domain of the complex plane of large quadratic eigenvalue problems (QEPs). The SS-RR method can suffer from numerical instability when the coefficient matrices of the projected QEP vary widely in norm. To improve the numerical stability of the SS-RR method, we combine it with a numerically...

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm "optimize first, then discretize" and relies on the approximation of the necessary optimality conditions in terms of the associated...

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh–Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impac...

In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second appro...