We give new versions of the global Newton method and the Kellogg & Li & Yorke method for calculating zero points and fixed points of nonlinear maps, which are numerically stable, but do not require an extra homotopy dimension. In addition, regularity results are established so that predictor-corrector continuation methods will lead to solutions if appropriate boundary conditions are satisfied.

UNLABELLED A Seventh-Order Linear Multistep Method (SOLMM) is developed and implemented in both predictor-corrector mode and block mode. The two approaches are compared by measuring their total number of function evaluations and CPU times. The stability property of the method is examined. This SOLMM is also compared with existing methods in the literature using standard numerical examples. AM...

The reaction path connects a chemical potential energy landscape and the conceptual descriptions of chemical mechanisms and reactivity. In recent years, a class of predictor-corrector integrators has been developed and shown to provide an excellent compromise between computational efficiency and numerical accuracy. Models based on projected frequencies along the reaction path and coupling matri...

The article presents a new scalable iterative method for linear programming called the “apex method”. key feature of this is constructing path close to optimal on surface feasible region from certain starting point exact solution problem. refers minimum length according Euclidean metric. apex based predictor—corrector framework and proceeds in two stages: quest (predictor) target (corrector). s...

Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O’Leary proposed a constraint-reduced predictor-corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraintreduced algorithm for semidefinite programmi...

In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...

An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector), which assigns importance weights to describe a non-Gaussian distribution. The importance weights are obtained by nonparametric density estimation. It is demonstrated on several numerical examples that the new predictor-corrector filter combines the advantag...

This paper proposes an improved predictor-corrector interior-point algorithm for the linear complementarity problem LCP based on the Mizuno-Todd-Ye algorithm. The modified corrector steps in our algorithm cannot only draw the iteration point back to a narrower neighborhood of the center path but also reduce the duality gap. It implies that the improved algorithm can converge faster than the MTY...

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature func...