Newton-Krylov methods, primarily using the Jacobian-Free Newton-Krylov (JFNK) approximation, are examined as an alternative to the traditional power iteration method for the calculation of the fundamental eigenmode in reactor analysis applications based on diffusion theory. One JFNK approach can be considered an acceleration technique for the standard power iteration as it is “wrapped around” t...

Neural Network Learning algorithms based on Conjugate Gradient Techniques and Quasi Newton Techniques such as Broyden, DFP, BFGS, and SSVM algorithms require exact or inexact line searches in order to satisfy their convergence criteria. Line searches are very costly and slow down the learning process. This paper will present new Neural Network learning algorithms based on Hoshino's weak line se...

The multilevel iterative technique is a powerful technique for solving systems of equations associated with discretized partial diierential equations. We describe how this techniques can be combined with a globally con-vergent approximate Newton method to solve nonlinear partial diierential equations. We show that asymptotically only one Newton iteration per level is required; thus the complexi...

In this paper, Field-Programmable Gate Array (FPGA) implementation-based image demosaicing is carried out. The Newton Gregory interpolation algorithm designed based on FPGA frame work. Interpolation the method of assessing value a function for any in-between self-regulating variable, whereas computing outside specified range named extrapolation. natural images are collected from Kodak database ...

A new hybrid technique for optimization of a multivariable function is proposed. This method is applied to the problem of complex time Green’s function of multilayer media. This technique combines Particle Swarm search algorithm with the gradient based quasi-Newton method. Superiority of the method is demonstrated by comparing its results with other optimization techniques.

In this paper we examine the sensitive dependence on the initial conditions of the Newton-Raphson search technique. It is demonstrated that this sensitivity has a fractal nature which can be effectively utilized to find all solutions to a nonlinear equation. The developed technique uses an important feature of fractals to preserve shape of basins of attraction on infinitely small scales.

Defining a consistent technique for maintaining the positive definiteness of the matrices generated by quasi-Newton methods for equality constrained minimization remains a difficult open problem. In this paper, we review and discuss the results obtained with a new technique based on an extension of the Wolfe line-search used in unconstrained optimization. The idea is to follow a piecewise linea...

This work is devoted to the study of integration with respect to binomial measures. We develop interpolation quadrature rules and study their properties. Applying a local error estimate based on null rules, we test two automatic integrators with local quadrature rules that generalize the five points Newton Cotes formula.