We propose a uniied analysis for a class of infeasible-start predictor-corrector algorithms for semideenite programming problems, using the Monteiro-Zhang uniied direction. The algorithms are direct generalizations of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. We show that the algorithms belonging to this class are globally convergent, provided the problem has a so...

The “Echo” method, elaborated by Adamczyk, which is commonly applied in many logopaedic clinics, requires the use of the delayed auditory feedback. The devices which perform this task may nowadays be replaced with a typical computer equipped with a sound set and delaying programme. In the article the authors present a real-time application, implemented on the basis of standard sound functions s...

Abstract In this work, we develop a class of high‐order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite‐Birkhoff‐Predictor‐Corrector (HBPC) and technique relaxation for numerical ordinary differential equations (ODEs). We explain algorithm in detail show results two‐ three‐derivative metho...

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...

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point; then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory; it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this p...

We study a generalization of the notion of Gaussian free field (GFF). Although the extension seems minor, we first show that a generalized GFF does not satisfy the spatial Markov property, unless it is a classical GFF. In stochastic homogenization, the scaling limit of the corrector is a possibly generalized GFF described in terms of an “effective fluctuation tensor” that we denote by Q. We pro...

We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the so...

The ideal location for an aberration corrector in an electron-optical column is at the place where the aberration is introduced. In practice, this of course typically cannot be achieved. The resultant separation between where an aberration is introduced and where it is removed produces combination aberrations for all aberrations of higher than first order. In the case of third-order aberration ...

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...

We introduce a new class of numerical schemes for the solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs). Our algorithms are of the predictor-corrector type; they are obtained via the decomposition of the solutions of the ODEs into combinations of appropriately chosen exponentials, whereas the classical schemes are based on the approximation of solutions by poly...