In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

There are numerous methods of post-processing that make use of iterative techniques. Many of these schemes have been demonstrated to be very effective at removing artifacts from compressed video, producing better and better image estimates at each iteration. However, this artifact removal comes at the cost of a large computational burden. This paper introduces two methods for iterative post-pro...

The fundamental idea behind all multigrid methods is to compute using diierent scales in order to obliterate error components of diierent scales. Error components can be thought of as waves. A long wave, which has low frequency, on one grid is a short wave, or high frequency, on a coarse enough related grid. A number of iterative methods (e.g., relaxation and alternating direction implicit meth...

This paper provides a detailed discussion of the second covariant derivative of a map and its role in the Lie group projection operator approach (a direct method for solving continuous time optimal control problems). We begin by briefly describing the iterative geometric optimal control algorithm and summarize the general expressions involved. Particular emphasis is placed on the expressions re...

A nonlinear system with two degrees of freedom consisting of a rigid platform and mechanical vibroactuator is considered. The platform, connected to an immovable base by means of elastic and damping elements can move along a fixed direction. The mechanical vibroactuator is an unbalanced rotor, mounted on the platform and driven with an electric drive. Such a system is a model of many vibrationa...

In many geometric modeling paradigms the user sculpts a curve or surface by dragging around some type of control points (eg. Bezier or B-spline). A more intuitive modeling interface allows the user to directly manipulate curves and surfaces. This manipulation defines some set of constraints that the curve or surface must satisfy (such as interpolation and tangent constraints). Direct manipulati...

We study nonlocal variational problems in Lp, like those that appear in peridynamics. The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions of either a convexity notion of the integrand, or a Jensen inequality for Young measures. Existence results, obtained through the direct ...

In almost every engineering and technology fields, information channel capacity is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel. Brijpaul and Sharma [1] gave a direct method of computing the performance function of a discrete memoryless communication channels. They obtained the performance function for discrete channels by ...