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In this paper, the global minimization problem of a multi-dimensional black-box Lipschitzian function is considered. In order to pass from the original Lipschitz multi-dimensional problem to a univariate one, an approach using space-filling curves to reduce the dimension is applied. The method does not use derivatives and, at each iteration, works with a set of estimates of the Hölder constant of the reduced one-dimensional problem. A two-phase technique is applied to accelerate the search of the global minimum. Numerical experiments carried out on several hundreds of test functions show a promising performance of the discussed algorithm in comparison with its direct competitors. [ABSTRACT FROM AUTHOR]

The subject of the paper is to analyze the possibilities of A* based algorithms performance regarding to the metric used to calculate the distances between two objects. The following algorithms have been selected: A*, IDA* (Iterative-Deepening A*) a SMA* (Simplified Memory-Bounded A*). Experimentally, the ability of these algorithms was studied considering to find the shortest path to the target, their ability to deal effectively with obstacles and two tests were focused on testing the load and its influence on the algorithm run. Each of the tests was also aimed at comparing the influence of Euclidean and Manhattan distances, the selection of which in some cases had a major impact on the effectiveness of the algorithm. All achieved results were summarized in the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, the Restricted additive Schwarz (RAS) method is applied to solve Helmholtz equation. To accelerate the RAS iterations, we propose to apply the vector ε-algorithm. Some convergence analysis of the proposed method is presented, and applied succeffully to Helmholtz problem. The obtained results show the effciency of the proposed approach. Moreover, the algorithm yields much faster convergence than the classical Schwarz iterations. [ABSTRACT FROM AUTHOR]

The iterative Induced Dimension Reduction (IDR) methods are considered for solving large systems of linear algebraic equations (SLAEs) with nonsingular nonsymmetric matrices. These approaches are investigated by many authors and are charachterized sometimes as the alternative to the classical processes of Krylov type. The key moments of the IDR algorithms consist in the construction of the embedded Sonneveld subspaces, which have the decreasing dimensions and use the orthogonalization to some fixed subspace. Other independent approaches for research and optimization of the iterations are based on the augmented and modified Krylov subspaces by using the aggregation and deflation procedures with present various low rank approximations of the original matrices. The goal of this paper is to show, that IDR method in Sonneveld subspaces present an original interpretation of the modified algorithms in the Krylov subspaces. In particular, such description is given for the multi-preconditioned semi-conjugate direction methods which are actual for the parallel algebraic domain decomposition approaches. [ABSTRACT FROM AUTHOR]

The Broyden family method for unconstrained optimization is known as one of the most efficient method in solving unconstrained optimization problem. Step size and search direction play the most important role to the convergence of the Broyden family method. Step size is proved to be successful method to solve the problem; however, it is definite to solve some complicated optimization problems. In this paper, we introduced the alternative procedure in determining the step size. This alternative procedure will be applied in the hybrid Broyden method. The numerical results based on number of iterations, number of gradient evaluation and number of function evaluation are given at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, a modification of spectral conjugate gradient (CG) method is proposed which combines the advantages of the spectral CG method and the RMIL method namely as spectral Khadijah-Rivaie-Mustafa-Ibrahim (SKRMI) to solve unconstrained optimization problems. Based on inexact line searches, the objective function generates a sufficient descent direction and the global convergence property for the proposed method has been proved. Moreover, the method reduces to the standard RMIL method if exact line search is applied. Numerical results are also presented to examine the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes the Interval Zoro-Symmetric Single-Step Procedure IZSS2-5D which is an extension of the previously proposed procedure IZSS2. It is also an extension of our procedure ISS2-5D. This procedure is developed in order to enhance the rate of convergence. Numerical results are obtained and they indicated that the IZSS2-5D outperformed the ISS2-5D in terms of computational time and number of iterations. [ABSTRACT FROM AUTHOR]

The main object of investigation of the paper is so called differential equation with "maxima". These equations, for example, find a wide application in the theory of automatic regulation. The main characteristic of this type of equations is the presence of the maximum of the unknown function over a past time interval. A nonlinear boundary value problem mixed with an initial condition for a nonlinear equation is studied. An algorithm for constructing two sequences of successive approximations of the solution is given. This algorithm is based on the monotone iterative technique combined by the method of lower/upper solutions. Each term of the constructed sequences is a solution of an initial value problem for linear differential equations with "maxima". Also the terms of the sequences are lower/upper solutions of the given problem. It is proved both sequences are monotonically convergent. The suggested procedure is illustrated on some examples. [ABSTRACT FROM AUTHOR]

Do Positron emission particle tracking (PEPT) has been used to track the motion of a single radioactively labeled tracer particle within a bed of similar particles. In this paper, the effect of the original event fraction on the results precise in two experiments has been reviewed. Results showed that the algorithm can no longer distinguish some corrupt trajectories, in addition to; further iteration reduces the statistical significance of the sample without improving its quality. Results show that the optimum value of trajectories depends on the type of experiment. [ABSTRACT FROM AUTHOR]

Lens-based imaging is able to directly provide an image of objects. The high quality lenses required, however, are not readily available for x-rays. Coherent diffraction imaging (CDI) bypasses this difficulty by numerically inverting the diffraction process undertaken by an object wave. The current CDI methods still face difficulties such as demanding experimental requirements in data collection and sample-dependent, unreliable convergence in their iterative reconstruction. Recently, we have proposed a new method to resolve these problems. The method employs a modulator and a novel phasing algorithm. Unlike imaging lenses or mirrors, the modulator can take various forms; therefore, it has less demanding requirements on its fabrication. In this paper, we describe more details about the technique. [ABSTRACT FROM AUTHOR]

Integer goal programming problems arise quite naturally in many real-world applications. In this paper, we propose a reference direction approach and interactive algorithm to solve integer goal programming problem. We use analytic hierarchy process (AHP) to get the reference direction. At each iteration, only one integer linear programming problem is solved to get an efficient solution. Through analytic hierarchy process the decision maker has to provide the preference point such that the original problem has been transformed into linear integer programming model. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic Nash games for weakly coupled large-scale systems with state-dependent noise are considered. The considered stochastic algebraic Riccati equations is quite different from the existing results in the sense that the equations have the additional linear term. The numerical algorithm based on Lyapunov iterations for solving the set of cross-coupled stochastic algebraic Riccati equations is derived by Mukaidani (American Control Conference, June 2008, USA 4232-4237). We modify this method and derive new iterations based on the solution of linear matrix equations with linear rate of convergence. We carry out numerical experiments to illustrate the effectiveness of the considered iterations. [ABSTRACT FROM AUTHOR]

Numerical methods are implemented in digital computers using finite precision arithmetics, in which real/complex numbers are represented by finite length words. This representation results in truncating/rounding off the numbers, which leads to numerical errors in the algorithms. The numerical errors can result in the loss of some properties of the numerical methods (for example, the orthogonality of the residues of the conjugate gradient), which, in turn, cause numerical instability. In this paper, a new model of the perturbations resulting from the use of finite precision arithmetic is proposed, based on a combination of the floating point model with the usual model of multiplicative perturbations at the input of a plant. This control perspective, applied to the classical problem of numerical perturbations due to finite precision, allows application of the well known small gain theorem of robust control theory in order to determine measures of the robustness or numerical stability of numerical algorithms. [ABSTRACT FROM AUTHOR]

This paper reports on the performance of a high resolution implemented as part of an implicit fully coupled velocity-pressure algorithm for the solution of laminar incompressible flow problems. The numerical implementation of high resolution convective schemes follows two techniques; (i) the Deferred Correction (DC) approach, and (ii) the Normalized Weighting Factor (NWF) method. The superiority of the NWF method over the DC approach is demonstrated by solving the sudden expansion in a square cavity problem. Results indicate that the number of iterations needed by the NWF solver is grid independent. Moreover, recorded CPU time values reveal that the NWF method substantially reduces the computational cost. [ABSTRACT FROM AUTHOR]

In this work, we introduce and study a new system of completely generalized multi-valued variational inclusions in uniformly smooth Banach spaces. By using the resolvent operator technique associated with m-accretive mappings, we propose an iterative algorithm for computing the approximate solutions of system of completely generalized multi-valued variational inclusions. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of system of completely generalized multi-valued variational inclusions. The results in this paper unify, extend and improve some known results from the literature. [ABSTRACT FROM AUTHOR]

This paper introduces a modification on the movement force vector of the Birbil and Fang’s electromagnetism-like algorithm [1] for solving global optimization problems with bounded variables. The proposed movement vector combines the total force exerted on each point of the population, at the current iteration, with the rate of change in the force vector of a previous iteration. Several widely used benchmark problems were solved to compare the proposed modification with the original algorithm. A performance profile assessment shows the efficiency and robustness of the proposed modification. [ABSTRACT FROM AUTHOR]

In this paper we propose two-grid algorithms for implementation of the A.M.Il’in’s scheme to diffusion convection-dominated equations. To find the solution from nonlinear algebraic systems we investigate Newton and Picard iterative methods. We offer to use the difference scheme on a coarse mesh and, using uniform interpolation, taking into account the boundary layers, to find suitable initial iteration for an iterative method on a fine mesh. We estimate the accuracy of the proposed algorithms and we count the number of the arithmetic operations. Numerical experiments illustrate the efficiency of these algorithms. [ABSTRACT FROM AUTHOR]

Image deconvolution is a powerful tool for improving the quality of images corrupted by blurring and noise. However, in some cases, the imaging system is affected by anisotropic resolution, i. e. the resolution depends on the direction in the imaging plane or volume. Such a distortion cannot be corrected by image deconvolution. One example, from Astronomy, is the Large Binocular Telescope (LBT) under construction on the top of Mount Graham (Arizona). A second example, from Microscopy, is the confocal microscope. In both cases, the situation can be improved if different images of the same target can be detected by rotating the instrument or by rotating the target. Then the problem arises of obtaining a unique high-resolution image from different images taken at different orientation angles. Such a problem is called multiple-image deconvolution. In this paper, after a brief illustration of the two examples mentioned above, the problem of multiple-image deconvolution is formulated and preliminarily investigated in a continuous setting (all directions are available), showing that, while resolution is anisotropic in the multiple images, it becomes isotropic in the reconstructed image. Next, methods and algorithms for the solution of the problem are presented and their accuracy illustrated by means of the results of a few numerical experiments. Finally, the possibility of a further improvement of resolution by means of super-resolving methods is briefly discussed and demonstrated. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, an improved random bit recycle multi-bit quantification algorithm based on Logistic mapping was proposed to resolve the high calculation complexity problem in generating stochastic sequence by using chaotic iteration and to improve the performance of the sequence. The balance and correlation property of the generated sequence were analyzed. The sequence was proved to obey the binary Bernoulli stochastic distribution and the auto and cross correlation was proved to obey normal distribution N(0,1/N). The simulation results indicate that the algorithm has excellent balance and correlation property. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]