Piecewise algebraic B-spline surfaces (ABS surfaces) are capable of modeling globally smooth shapes of arbitrary topology. These can be potentially applied in geometric modeling, scientific visualization, computer animation and mathematical illustration. However, real-time ray casting the surface is still an obstacle for interactive applications, due to the large amount of numerical root findin...

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness our method, we perform numerical experiments that number iterations scales square root condition number, and also compare existing state-of-the-art quasi-Newton methods on Stiefel manifold. Our show outperforms some large, ill-c...

in this work, a hybrid gmdh–neural network model was developed in order to predict the moisture content of papaya slices during hot air drying in a cabinet dryer. for this purpose, parameters including drying time, slices thickness and drying temperature were considered as the inputs and the amount of moisture ratio (mr) was estimated as the output. exactly 50% of the data points were used for ...

We consider the problem of computing square root a perturbation scaled identity matrix, , where and are matrices with . This arises in various applications, including computer vision optimization methods for machine learning. derive new formula th that involves weighted sum powers matrix is particularly attractive root, since has just one term when also class Newton iterations exploit low-rank ...

This paper addresses the problem of nonlinear multivariate root nding. In an earlier paper we describe a system called Newton which nds roots of systems of nonlinear equations using re nements of interval methods. The re nements are inspired by AI constraint propagation techniques. Newton is competitive with continuation methods on most benchmarks and can handle a variety of cases that are infe...

Newton’s iteration has quadratic convergence for simple roots. We present a Newton-based iteration scheme with quadratic convergence for multiple roots of systems of analytic functions. This is a report on work in progress. 1. Newton Iteration, Approximate Roots and γ-Theorems 1.1. Newton Iteration. Let f : Cn → Cn be an analytic function. Newton’s method for solving f = 0 consists in approxima...

in this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear fredholm integral equations of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.