We consider three steps numerical integrator which is derived by collocation and interpolation of power series approximation solution to generate a linear multistep method which serves as the corrector. The corrector is then implemented in block method. We then propose another numerical integrator which is implemented in block method to serve as a constant order predictor to the corrector. Basi...

We establishe the polynomial convergence of a new class of pathfollowing methods for linear complementarity problems (LCP). Namely, we show that the predictor-corrector methods based on the L2 norm neighborhood. Mathematics Subject Classification: 90C33, 65G20, 65G50

In this paper, a new predictor-corrector method is proposed for solving sufficient linear complementarity problems (LCP) with an infeasible starting point. The method generates a sequence of iterates in a wide and symmetric neighborhood of the infeasible central path of the LCP. If the starting point is feasible or close to being feasible, then an ε-approximate solution is obtained in at most O...

Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our a...

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative methods for solving nonlinear equations of the type f(x) = 0 by using the technique of updating the solution. This method can be viewed as a predictor– corrector iterative Halley’s method. We also consider the convergence analysis of the proposed method. To illustrate the efficiency of this new method, we gi...

Motivated by a numerical example which shows that a feasible version of Mehrotra’s original predictor-corrector algorithm might be inefficient in practice, Salahi et al., proposed a so-called safeguard based variant of the algorithm that enjoys polynomial iteration complexity while its practical efficiency is preserved. In this paper we analyze the same Mehrotra’s algorithm from a different per...

Two corrector-predictor interior point algorithms are proposed for solving monotone linear complementarity problems. The algorithms produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first algorithm uses line search schemes requiring the solution of higher order polynomial equations in one variable, while the line search procedures of the second algorithm can be im...

This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of recentering in the implementation of interior point methods. Second-order correctors, such as Mehrotra’s predictor–corrector, can occ...