The improved versions of the Kung–Traub family and the Zheng–Li–Huang family of n-point derivative free methods for solving nonlinear equations are proposed. The convergence speed of the modified families is considerably accelerated by employing a self-correcting parameter. This parameter is calculated in each iteration using information from the current and previous iteration so that the propo...

We show that the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm with projection may exhibit slow convergence in constrained stochastic optimization problems when the optimum is situated on the constraints. The cause of the slow convergence is a geometric interaction between the projection operator and the SPSA gradient estimate. The effect of this interaction can be describ...

Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin’s projection approach. The free surface between the two fluid phases is tracked with a level set technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated us...

We study convergence of a boundary integral method for 3D interfacial flow with surface tension when the fluid velocity is given by Darcy’s Law. The method is closely related to a previous method developed and implemented by Ambrose, Siegel, and Tlupova, in which one of the main ideas is the use of an isothermal parameterization of the free surface. We prove convergence by proving consistency a...

We prove the almost sure convergence to zero of the uctuations of the free energy, resp. local free energies, in a class of disordered mean-eld spin systems that generalize the Hoppeld model in two ways: 1) Multi-spin interactions are permitted and 2) the random variables i describing thèpatterns' can have arbitrary distributions with mean zero and nite 4+-th moments. The number of patterns, M,...

In recent work, Chow, Huang, Li and Zhou [6] introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When N ≥ 2 is the number of vertices of the graph, they show that the corresponding FokkerPlanck equation is a system of N nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices ...

The convergence of (diagonal) sequences of rational interpolants to an analytic function is investigated. Problems connected with their definition are shortly discussed. Results about locally uniform convergence are reviewed. Then the convergence in capacity is studied in more detail. Here, a central place is taken by a theorem about the convergence in capacity of rational interpolants to funct...

We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A∗X−1A = Q and X − A∗X−1A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton’s method and inversion free variants of the basic fixed point iteration are discussed in some detail for the...

We develop n-point optimal derivative-free root finding methods of order 2n, based on the Hermite interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that the optimal order of convergence of the transformed methods is preserved, according to the conjecture of Kung and Traub. To check the effectiveness and reliability of the newly presented method...

Term “super-resolution” is typically used for a high-resolution image produced from several low-resolution noisy observations. In this paper, we consider the problem of high-quality interpolation of a single noise-free image. Several aspects of the corresponding super-resolution algorithm are investigated: choice of regularization term, dependence of the result on initial approximation, converg...