In this paper, we present two new one-step iterative methods based on Thiele’s continued fraction for solving nonlinear equations. By applying the truncated Thiele’s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two...

This paper addresses certain inherent limitations of local priority hysteresis switching logic. Our main result establishes that under persistent excitation assumption, it is possible to relax constraints requiring strict positivity of local priority and hysteresis switching constants. Relaxing these constraints allows the adaptive system to reach optimality which implies the performance improv...

Sfinks is a shift register based stream cipher designed for hardware implementation. The initialisation state update function is different from the state update function used for keystream generation. We demonstrate state convergence during the initialisation process, even though the individual components used in the initialisation are one-to-one. However, the combination of these components is...

As physical and information security boundaries have become increasingly blurry many organizations are experiencing challenges with how to effectively and efficiently manage security within the corporate. There is no current standard or best practice offered by the security community regarding convergence; however many organizations such as the Alliance for Enterprise Security Risk Management (...

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very larg...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

L 2 boundary decay properties of the heat kernel and spectral density. We deduce bounds on the rate of convergence of the eigenvalues when the region is slightly reduced in size. It is remarkable that several of the bounds do not involve the space dimension. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: boundary decay, Laplacian, Hardy inequality, eigenfunctions, heat kernel...

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some pre...

This paper is a sequel to both Ash, Erd1⁄2os and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the Ash-Erd1⁄2os-Rubel approach –imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property – lead naturally to the main result of regular variation, th...

we present and study the stability and convergence, and order of convergence of a numerical scheme used in geophysics, namely, the stochastic version of a deterministic “implicit leapfrog” scheme which has been developed for the approximation of the socalled barotropic vorticity model. Two other schemes which might be useful in the context of geophysical applications are also introduced and dis...