A NEW CLASS OF TWO-STEP ITERATIVE ALGORITHMS FOR FINDING THE ROOTS OF NONLINEAR EQUATIONS
GREGORY ANTONI *
Aix-Marseille Universite, IFSTTAR, LBA UMR T24, F-13016 Marseille, France
*Author to whom correspondence should be addressed.
This study deals with a new class of two-step iterative algorithms for solving nonlinear equations. These algorithms are based on high order Newton-type methods in order to improve the convergence of the approximate solution of the root of the nonlinear equations under consideration. Derived from the iterative-type schemes with two-steps, three algorithms are proposed and the associated convergence analysis is also addressed. Finally, the presented algorithms are implemented in the Matlab software and then tested and evaluated on some simple examples.
Keywords: Nonlinear equations, Newton's algorithm, two-step iterative algorithm, convergence analysis