ISRN Computational Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Analysis of General Input State Dependent Working Vacation Queue with Changeover Time Wed, 23 Apr 2014 13:42:35 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2014/248704/ We consider a finite buffer queue with multiple working vacations and changeover time, where the server can keep on working but at a slower speed during the vacation period. Moreover, the amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. Finally, some numerical results of the model are presented to show the parameter effect on various performance measures. Vijaya Laxmi Pikkala and Suchitra Vepada Copyright © 2014 Vijaya Laxmi Pikkala and Suchitra Vepada. All rights reserved. Some Derivative-Free Quadrature Rules for Numerical Approximations of Cauchy Principal Value of Integrals Mon, 17 Mar 2014 17:30:19 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2014/186397/ Some derivative-free six-point quadrature rules for approximate evaluation of Cauchy principal value of integrals have been constructed in this paper. Rules are numerically verified by suitable integrals, their degrees of precision have been determined, and their respective errors have been asymptotically estimated. Rabindranath Das, Manoj Kumar Hota, and Manoranjan Bej Copyright © 2014 Rabindranath Das et al. All rights reserved. Powers of Complex Persymmetric Antitridiagonal Matrices with Constant Antidiagonals Sun, 16 Mar 2014 08:15:05 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2014/451270/ We derive a general expression for the pth power of any complex persymmetric antitridiagonal Hankel (constant antidiagonals) matrices. Numerical examples are presented, which show that our results generalize the results in the related literature (Rimas 2008, Wu 2010, and Rimas 2009). Haibo Wang Copyright © 2014 Haibo Wang. All rights reserved. Preconditioned Krylov Subspace Methods for Sixth Order Compact Approximations of the Helmholtz Equation Tue, 21 Jan 2014 09:55:59 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2014/745849/ We consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann, and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and lower order preconditioned Krylov subspace methodology. The resulting systems of finite-difference equations are solved by different preconditioned Krylov subspace-based methods. In the analysis of the lower order preconditioning developed here, we introduce the term “kth order preconditioned matrix” in addition to the commonly used “an optimal preconditioner.” The necessity of the new criterion is justified by the fact that the condition number of the preconditioned matrix in some of our test problems improves with the decrease of the grid step size. In a simple 1D case, we are able to prove this analytically. This new parameter could serve as a guide in the construction of new preconditioners. The lower order direct preconditioner used in our algorithms is based on a combination of the separation of variables technique and fast Fourier transform (FFT) type methods. The resulting numerical methods allow efficient implementation on parallel computers. Numerical results confirm the high efficiency of the proposed iterative approach. Yury Gryazin Copyright © 2014 Yury Gryazin. All rights reserved. Fixed Point Theorems and Error Bounds in Partial Metric Spaces Tue, 31 Dec 2013 10:39:30 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/184026/ This paper is introduced as a survey of result on some generalization of Banach’s fixed point and their approximations to the fixed point and error bounds, and it contains some new fixed point theorems and applications on dualistic partial metric spaces. S. A. M. Mohsenalhosseini Copyright © 2013 S. A. M. Mohsenalhosseini. All rights reserved. Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices Thu, 12 Dec 2013 07:53:48 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/249594/ The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters. Nicholas Assimakis and Maria Adam Copyright © 2013 Nicholas Assimakis and Maria Adam. All rights reserved. Applying Cubic B-Spline Quasi-Interpolation to Solve 1D Wave Equations in Polar Coordinates Sat, 07 Dec 2013 14:53:03 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/710529/ We provide numerical solution to the one-dimensional wave equations in polar coordinates, based on the cubic B-spline quasi-interpolation. The numerical scheme is obtained by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a forward difference to approximate the time derivative of the dependent variable. The accuracy of the proposed method is demonstrated by three test problems. The results of numerical experiments are compared with analytical solutions by calculating errors -norm and -norm. The numerical results are found to be in good agreement with the exact solutions. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. Hossein Aminikhah and Javad Alavi Copyright © 2013 Hossein Aminikhah and Javad Alavi. All rights reserved. Soliton Solutions of the Klein-Gordon-Zakharov Equation with Power Law Nonlinearity Tue, 03 Dec 2013 17:52:35 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/716279/ We introduce a new version of the trial equation method for solving nonintegrable partial differential equations in mathematical physics. Some exact solutions including soliton solutions and rational and elliptic function solutions to the Klein-Gordon-Zakharov equation with power law nonlinearity in (1 + 2) dimensions are obtained by this method. Mehmet Ekici, Durgun Duran, and Abdullah Sonmezoglu Copyright © 2013 Mehmet Ekici et al. All rights reserved. A New Finite Element Method for Darcy-Stokes-Brinkman Equations Sun, 24 Nov 2013 13:34:28 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/798059/ We present a new finite element method for Darcy-Stokes-Brinkman equations using primal and dual meshes for the velocity and the pressure, respectively. Using an orthogonal basis for the discrete space for the pressure, we use an efficiently computable stabilization to obtain a uniform convergence of the finite element approximation for both limiting cases. Bishnu P. Lamichhane Copyright © 2013 Bishnu P. Lamichhane. All rights reserved. A Robust and Accurate Quasi-Monte Carlo Algorithm for Estimating Eigenvalue of Homogeneous Integral Equations Sun, 10 Nov 2013 15:13:36 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/891029/ We present an efficient numerical algorithm for computing the eigenvalue of the linear homogeneous integral equations. The proposed algorithm is based on antithetic Monte Carlo algorithm and a low-discrepancy sequence, namely, Faure sequence. To reduce the computational time we reduce the variance by using the antithetic variance reduction procedure. Numerical results show that our scheme is robust and accurate. F. Mehrdoust, B. Fathi Vajargah, and E. Radmoghaddam Copyright © 2013 F. Mehrdoust et al. All rights reserved. An Overview of Recent Research Results and Future Research Avenues Using Simulation Studies in Project Management Thu, 24 Oct 2013 08:15:55 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/513549/ This paper gives an overview of three simulation studies in dynamic project scheduling integrating baseline scheduling with risk analysis and project control. This integration is known in the literature as dynamic scheduling. An integrated project control method is presented using a project control simulation approach that combines the three topics into a single decision support system. The method makes use of Monte Carlo simulations and connects schedule risk analysis (SRA) with earned value management (EVM). A corrective action mechanism is added to the simulation model to measure the efficiency of two alternative project control methods. At the end of the paper, a summary of recent and state-of-the-art results is given, and directions for future research based on a new research study are presented. Mario Vanhoucke Copyright © 2013 Mario Vanhoucke. All rights reserved. New Preconditioners for Nonsymmetric Saddle Point Systems with Singular Block Tue, 27 Aug 2013 13:21:14 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/507817/ We investigate the solution of large linear systems of saddle point type with singular block by preconditioned iterative methods and consider two parameterized block triangular preconditioners used with Krylov subspace methods which have the attractive property of improved eigenvalue clustering with increased ill-conditioning of the block of the saddle point matrix, including the choice of the parameter. Meanwhile, we analyze the spectral characteristics of two preconditioners and give the optimal parameter in practice. Numerical experiments that validate the analysis are presented. Qingbing Liu Copyright © 2013 Qingbing Liu. All rights reserved. Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces Thu, 23 May 2013 15:52:10 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/602579/ The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces. Satish Shukla, Ishak Altun, and Ravindra Sen Copyright © 2013 Satish Shukla et al. All rights reserved. Conditional Maximum Likelihood Estimation in Polytomous Rasch Models Using SAS Thu, 28 Mar 2013 09:13:00 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/617475/ IRT models are widely used but often rely on distributional assumptions about the latent variable. For a simple class of IRT models, the Rasch models, conditional inference is feasible. This enables consistent estimation of item parameters without reference to the distribution of the latent variable in the population. Traditionally, specialized software has been needed for this, but conditional maximum likelihood estimation can be done using standard software for fitting generalized linear models. This paper describes an SAS macro %rasch_cml that fits polytomous Rasch models. The macro estimates item parameters using conditional maximum likelihood (CML) estimation and person locations using maximum likelihood estimator (MLE) and Warm's weighted likelihood estimation (WLE). Graphical presentations are included: plots of item characteristic curves (ICCs), and a graphical goodness-of-fit-test is also produced. Karl Bang Christensen Copyright © 2013 Karl Bang Christensen. All rights reserved. Approximate Gröbner Bases, Overdetermined Polynomial Systems, and Approximate GCDs Thu, 21 Mar 2013 14:01:16 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/352806/ We discuss computation of Gröbner bases using approximate arithmetic for coefficients. We show how certain considerations of tolerance, corresponding roughly to absolute and relative error from numeric computation, allow us to obtain good approximate solutions to problems that are overdetermined. We provide examples of solving overdetermined systems of polynomial equations. As a secondary feature we show handling of approximate polynomial GCD computations, using benchmarks from the literature. Daniel Lichtblau Copyright © 2013 Daniel Lichtblau. All rights reserved. Solving a Class of Singular Two-Point Boundary Value Problems Using New Modified Decomposition Method Thu, 21 Feb 2013 09:24:24 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/262863/ We introduce an effective methodology for solving a class of linear as well as nonlinear singular two-point boundary value problems. This methodology is based on a modification of Adomian decomposition method (ADM) and a new two fold integral operator. We use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components of solution. Thus, we develop modified recursive scheme without any undetermined coefficients while computing the successive solution components. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. However, most of earlier recursive schemes using ADM do require computation of undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the present technique. The results reveal that the method is very effective, straightforward, and simple. Randhir Singh and Jitendra Kumar Copyright © 2013 Randhir Singh and Jitendra Kumar. All rights reserved. Radiation Effects on Mass Transfer Flow through a Highly Porous Medium with Heat Generation and Chemical Reaction Wed, 20 Feb 2013 11:32:44 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/765408/ The present paper is concerned to analyze the influence of the unsteady free convection flow of a viscous incompressible fluid through a porous medium with high porosity bounded by a vertical infinite moving plate in the presence of thermal radiation, heat generation, and chemical reaction. The fluid is considered to be gray, absorbing, and emitting but nonscattering medium, and Rosseland approximation is considered to describe the radiative heat flux in the energy equation. The dimensionless governing equations for this investigation are solved analytically using perturbation technique. The effects of various governing parameters on the velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are shown in figures and tables and analyzed in detail. S. Mohammed Ibrahim Copyright © 2013 S. Mohammed Ibrahim. All rights reserved. Some New Explicit Values of Parameters and of Quotients of Eta-Function Mon, 18 Feb 2013 09:34:18 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/435261/ We find some new explicit values of the parameters and of quotients of eta-function by using Ramanujan's class invariants. Nipen Saikia Copyright © 2013 Nipen Saikia. All rights reserved. Evolutionary Algorithms for Robust Density-Based Data Clustering Thu, 17 Jan 2013 15:46:24 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2013/931019/ Density-based clustering methods are known to be robust against outliers in data; however, they are sensitive to user-specified parameters, the selection of which is not trivial. Moreover, relational data clustering is an area that has received considerably less attention than object data clustering. In this paper, two approaches to robust density-based clustering for relational data using evolutionary computation are investigated. Amit Banerjee Copyright © 2013 Amit Banerjee. All rights reserved. The Middle Pivot Element Algorithm Mon, 31 Dec 2012 17:32:07 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/947634/ This paper is an improvement over the previous work on New Sorting Algorithm first proposed by Sundararajan and Chakraborty (2007). Here we have taken the pivot element as the middle element of the array. We call this improved version Middle Pivot Element Algorithm (MPA) and it is found that MPA is much faster than the two algorithms RPA (Random Pivot element Algorithm) and FPA (First Pivot element Algorithm) in which the pivot element was selected either randomly or as the first element, respectively. Anchala Kumari and Soubhik Chakraborty Copyright © 2012 Anchala Kumari and Soubhik Chakraborty. All rights reserved. High Performance Gibbs Sampling for IRT Models Using Row-Wise Decomposition Wed, 12 Dec 2012 15:40:00 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/264040/ Item response theory (IRT) is a popular approach used for addressing statistical problems in psychometrics as well as in other fields. The fully Bayesian approach for estimating IRT models is computationally expensive. This limits the use of the procedure in real applications. In an effort to reduce the execution time, a previous study shows that high performance computing provides a solution by achieving a considerable speedup via the use of multiple processors. Given the high data dependencies in a single Markov chain for IRT models, it is not possible to avoid communication overhead among processors. This study is to reduce communication overhead via the use of a row-wise decomposition scheme. The results suggest that the proposed approach increased the speedup and the efficiency for each implementation while minimizing the cost and the total overhead. This further sheds light on developing high performance Gibbs samplers for more complicated IRT models. Yanyan Sheng and Mona Rahimi Copyright © 2012 Yanyan Sheng and Mona Rahimi. All rights reserved. A New 5-Point Ternary Interpolating Subdivision Scheme and Its Differentiability Wed, 14 Nov 2012 09:23:22 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/924839/ A new 5-point ternary interpolating scheme with a shape parameter is introduced. The resulting curve is for a certain range of parameters. The differentiable properties of the proposed scheme to extend its application in the generation of smooth curves are explored. Application of the proposed scheme is given to show its visual smoothness. The scheme is also extended to a 5-point tensor product ternary interpolating scheme, and its numerical examples are also included. Ghulam Mustafa, Jayyada Irum, and Mehwish Bari Copyright © 2012 Ghulam Mustafa et al. All rights reserved. A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities Mon, 05 Nov 2012 09:45:53 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/171606/ This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method. V. Krishna Rao Kandanvli and Haranath Kar Copyright © 2012 V. Krishna Rao Kandanvli and Haranath Kar. All rights reserved. Study of Stationary Load Increase of Computer-Network Traffic via Dynamic Principal-Component Analysis Sun, 16 Sep 2012 11:45:36 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/103509/ Many network monitoring applications and performance analysis tools are based on the study of an aggregate measure of network traffic, for example, number of packets in transit (NPT). The simulation modeling and analysis of this type of performance indicator enables a theoretical investigation of the underlying complex system through different combination of network setups such as routing algorithms, network source loads or network topologies. To detect stationary increase of network source load, we propose a dynamic principal component analysis (PCA) method, first to extract data features and then to detect a stationary load increase. The proposed detection schemes are based on either the major or the minor principal components of network traffic data. To demonstrate the applications of the proposed method, we first applied them to some synthetic data and then to network traffic data simulated from the packet switching network (PSN) model. The proposed detection schemes, based on dynamic PCA, show enhanced performance in detecting an increase of network load for the simulated network traffic data. These results show usefulness of a new feature extraction method based on dynamic PCA that creates additional feature variables for event detection in a univariate time series. Shengkun Xie and Anna T. Lawniczak Copyright © 2012 Shengkun Xie and Anna T. Lawniczak. All rights reserved. Consistent Neighborhood Search for Combinatorial Optimization Thu, 13 Sep 2012 17:20:55 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/671423/ Many optimization problems (from academia or industry) require the use of a local search to find a satisfying solution in a reasonable amount of time, even if the optimality is not guaranteed. Usually, local search algorithms operate in a search space which contains complete solutions (feasible or not) to the problem. In contrast, in Consistent Neighborhood Search (CNS), after each variable assignment, the conflicting variables are deleted to keep the partial solution feasible, and the search can stop when all the variables have a value. In this paper, we formally propose a new heuristic solution method, CNS, which has a search behavior between exhaustive tree search and local search working with complete solutions. We then discuss, with a unified view, the great success of some existing heuristics, which can however be considered within the CNS framework, in various fields: graph coloring, frequency assignment in telecommunication networks, vehicle fleet management with maintenance constraints, and satellite range scheduling. Moreover, some lessons are given in order to have guidelines for the adaptation of CNS to other problems. Michel Vasquez and Nicolas Zufferey Copyright © 2012 Michel Vasquez and Nicolas Zufferey. All rights reserved. A Comparative Study on the Stability of Laplace-Adomian Algorithm and Numerical Methods in Generalized Pantograph Equations Wed, 05 Sep 2012 15:43:52 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/704184/ The main objective of this paper is to examine the stability and convergence of the Laplace-Adomian algorithm to approximate solutions of the pantograph-type differential equations with multiple delays. This is done by comparatively investigating it with other methods. Sabir Widatalla Copyright © 2012 Sabir Widatalla. All rights reserved. Laplace Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Partial Differential Equation Tue, 04 Sep 2012 09:40:10 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/423469/ Analytical and numerical solutions are obtained for coupled nonlinear partial differential equation by the well-known Laplace decomposition method. We combined Laplace transform and Adomain decomposition method and present a new approach for solving coupled Schrödinger-Korteweg-de Vries (Sch-KdV) equation. The method does not need linearization, weak nonlinearity assumptions, or perturbation theory. We compared the numerical solutions with corresponding analytical solutions. Arun Kumar and Ram Dayal Pankaj Copyright © 2012 Arun Kumar and Ram Dayal Pankaj. All rights reserved. A Parameter for Ramanujan's Function χ(q): Its Explicit Values and Applications Tue, 14 Aug 2012 09:09:31 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/169050/ We define a new parameter πΌπ‘˜,𝑛 involving quotient of Ramanujan's function πœ’(π‘ž) for positive real numbers π‘˜ and 𝑛 and study its several properties. We prove some general theorems for the explicit evaluations of the parameter πΌπ‘˜,𝑛 and find many explicit values. Some values of πΌπ‘˜,𝑛 are then used to find some new and known values of Ramanujan's class invariant 𝐺𝑛. Nipen Saikia Copyright © 2012 Nipen Saikia. All rights reserved. A New Efficient Method for Solving Two-Dimensional Burgers' Equation Mon, 13 Aug 2012 09:38:44 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/603280/ We introduce a new hybrid of the Laplace transform method and new homotopy perturbation method (LTNHPM) that efficiently solves nonlinear two-dimensional Burgers’ equation. Three examples are given to demonstrate the efficiency of the new method. Hossein Aminikhah Copyright © 2012 Hossein Aminikhah. All rights reserved. Wavelet Kernel Principal Component Analysis in Noisy Multiscale Data Classification Sun, 29 Jul 2012 14:02:32 +0000 http://www.hindawi.com/journals/isrn.computational.mathematics/2012/197352/ We introduce multiscale wavelet kernels to kernel principal component analysis (KPCA) to narrow down the search of parameters required in the calculation of a kernel matrix. This new methodology incorporates multiscale methods into KPCA for transforming multiscale data. In order to illustrate application of our proposed method and to investigate the robustness of the wavelet kernel in KPCA under different levels of the signal to noise ratio and different types of wavelet kernel, we study a set of two-class clustered simulation data. We show that WKPCA is an effective feature extraction method for transforming a variety of multidimensional clustered data into data with a higher level of linearity among the data attributes. That brings an improvement in the accuracy of simple linear classifiers. Based on the analysis of the simulation data sets, we observe that multiscale translation invariant wavelet kernels for KPCA has an enhanced performance in feature extraction. The application of the proposed method to real data is also addressed. Shengkun Xie, Anna T. Lawniczak, Sridhar Krishnan, and Pietro Lio Copyright © 2012 Shengkun Xie et al. All rights reserved.