Keywords : Newton method


Parallel Newtonian Optimization without Hessian Approximation

Khalil K. Abbo

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 2, Pages 69-82
DOI: 10.33899/csmj.2006.164053

The purpose of this paper is to introduce parallel algorithms based on the Newton method for solving non-linear unconstrained optimization problem in (MIMD) parallel computers by solving linear system in parallel using Gaussian Elimination method rather than finding inverse Hessian matrix to avoid the errors caused by evaluating the inverse matrix and also to increase computing power and reduce run time.
 

A New Newton-Wavelet Algorithm to Solve Non-Linear Equations

Kais Ibraheem; Riyad M. Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 95-109
DOI: 10.33899/csmj.2006.164039

In this research, a new algorithm to solve the non-linear equations (f(x)=0) was developed. The new method was called Newton –Wavelet which can be defined as a mix between two methods, Newton and wavelet. By applying this algorithm on seven examples and compared the result with the Broyden method it has shown a good efficiency. The new method shows that it can decrease the number of iterations and then decrease the time needed to solve the used equations. This algorithms considered a new technique of mixes between two subjects the first one is a numerical analysis (by using Newton method) and the second is an image processing and data compression (by using Wavelet analysis), The basic aim of this research is decrease the time of solution.