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...

In this paper, we propose a simple variant of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming problem (LP). Our variants execute a natural finite termination procedure at each iteration and it is easy to implement the algorithm. Our algorithm admits an objective-function free polynomial-time complexity when it is applied to LPs whose dual feasible region is bounded.

A predictor-corrector method for solving linear programs from infeasible starting points is analyzed. The method is quadratically convergent and can be combined with Ye's finite termination scheme under very general assumptions. If the starting points are large enough then the algorithm has O(nL) iteration complexity. If the ratio between feasibility and optimality at the starting points is sma...

The higher order predictor (43) from [1] has to be modified in the degenerate case in order for the asymptotic convergence results from Lemma 4.6 and Theorem 4.7 to hold. More precisely equation (43) should be replaced by: where = 0 , if HLCP is nondegenerate 1 , if HLCP is degenerate. (2) The computational complexity results hold for the new algorithm, with slight modifications in the proof. C...

In this paper a one parameter predictor–corrector method, which we call it A-EBDF, is introduced and analyzed. With a modification of A-BDF and EBDF methods we propose a multistep method whose region of absolute stability is larger than those of A-BDF and EBDF methods. © 2004 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 65L05

In this paper, we propose a stable and efficient algorithm for animating mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid approximation of the implicit integration, t...

In this chapter, we propose a stable and efficient algorithm for animating cloth-like materials using mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid approximation o...

In this paper, we present an Adaptive Posicast Controller that deals with parametric uncertainties in linear systems with delays. It is assumed that the plant has no right half plane zeros and the delay is known. The adaptive controller is based on the Smith Predictor and Finite-Spectrum Assignment with time-varying parameters adjusted online. A novel Lyapunov-Krasovskii functional is used to s...

------

We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated [1]–[3] whose accumulated squared prediction error, for every bounded sequence, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a giv...