In this paper, we have obtained three optimal order Newton’s like methods of four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis all the is discussed separately. We corresponding conjugacy maps quadratic polynomials also extraneous fixed points. considered several test functions to examine explain dynamics our proposed methods. Theoretical results, numer...

In this paper, a reduced order local optimal controller is designed for a higher order system. A reduced order model is obtained for the higher order system and its parameters are used for the reduced order local optimal controller. Also, genetic algorithm is used with the reduced order local optimal controller structure to design the controller parameters instead of obtaining them from the red...

In a recent paper, Bubeck, Lee, and Singh introduced a new first order method for minimizing smooth strongly convex functions. Their geometric descent algorithm, largely inspired by the ellipsoid method, enjoys the optimal linear rate of convergence. We show that the same iterate sequence is generated by a scheme that in each iteration computes an optimal average of quadratic lower-models of th...