In this paper we discuss the use of block principal pivoting and predictor-corrector methods for the solution of large-scale linear least squares problems with nonnegative variables (NVLSQ). We also describe two implementations of these algorithms that are based on the normal equations and corrected seminormal equations (CSNE) approaches. We show that the method of normal equations should be em...

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...

This note points out an error in the local quadratic convergence proof of the predictorcorrector interior-point algorithm for solving the semidefinite linear complementarity problem based on the Alizadeh–Haeberly–Overton search direction presented in [M. Kojima, M. Shida, and S. Shindoh, SIAM J. Optim., 9 (1999), pp. 444–465]. Their algorithm is slightly modified and the local quadratic converg...

This paper proposes a globally convergent predictor-corrector infeasible-interiorpoint algorithm for the monotone semide nite linear complementarity problem using the AlizadehHaeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.

In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting   0 f x   near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of ...

distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we study numerical methods for hybrid fuzzy differential equations by an appllication of the Milne's fourth order predictor-corrector method for fuzzy differential equations. We prove a conv...

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra...

Interior point methods have been widely used to determine the solution of large-scale linear programming problems. The predictor-corrector method stands out among all variations of interior point methods due to its efficiency and fast convergence. In each iteration it is necessary to solve two linear systems to determine the predictor-corrector direction. Solving such systems corresponds to the...

In a recent paper, Noor and Noor [K. Inayat Noor, M. Aslam Noor, Predictor–corrector Halley method for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.11.023] have suggested and analyzed a predictor–corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which has a quintic convergence. W...