An optimised design of a radio frequency energy harvesting antenna is presented. The antenna is based on a compact ferrite rod which, together with the electronics, can directly replace batteries in suitable applications. The antenna is optimised such that the energy available for the applications is maximised, while considering constraints such as the device geometry and the Q ‐factor. That the antenna can power a wireless sensor node is shown from the ambient medium wave transmissions.

In this paper, we provide a detailed local convergence analysis of a one-parameter family of iteration methods for the simultaneous approximation of polynomial zeros due to Ivanov (Numer. Algor. 75(4): 1193–1204, 2017). Thus, we obtain two local convergence theorems that provide sufficient conditions to guarantee the Q-cubic convergence of all members of the family. Among the other contributions, our results unify the latest such kind of results of the well known Dochev–Byrnev and Ehrlich methods. Several practical applications are further given to emphasize the advantages of the studied family of methods and to show the applicability of the theoretical results.

In the present paper, we prove a new local convergence theorem with initial conditions and error estimates that ensure the Q-quadratic convergence of a modification of the famous Weierstrass method. Afterward, we prove a semilocal convergence theorem that is of great practical importance owing to its computable initial condition. The obtained theorems improve and complement all existing such kind of convergence results about this method. At the end of the paper, we provide three numerical examples to show the applicability of our semilocal theorem to some physics problems. Within the examples, we propose a new algorithm for the experimental study of the dynamics of the simultaneous methods and compare the convergence and dynamical behaviors of the modified and the classical Weierstrass methods.

In this paper, we present an effective two-stage numerical algorithm for the simultaneous finding of all roots of meromorphic functions in a region within the complex plane. At the first stage, we construct a polynomial with the same roots as the ones of the considered function; at the next step, we apply some method for the simultaneous approximation of its roots. To show the efficiency and applicability of our algorithm together with its advantages over the classical Newton, Halley and Chebyshev’s iterative methods, we conduct three numerical examples, where we apply it to two test functions and to an important engineering problem.