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To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A풱−풱‾B=C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast Alikhanov algorithm with nonuniform time steps for a two dimensional distributed‐order time–space fractional advection–dispersion equation. First, an efficient fast Alikhanov algorithm on the general nonuniform time steps for the evaluation of Caputo fractional derivative is presented to sharply reduce the computational work and storage, and are applied to the distributed‐order time fractional derivative or multi‐term time fractional derivative under the nonsmooth regularity assumptions. And a generalized discrete fractional Grönwall inequality is extended to multi‐term fractional derivative or distributed‐order fractional derivative for analyzing theoretically our algorithm. Then the stability and convergence of time semi‐discrete scheme are investigated. Furthermore, we derive the corresponding fully discrete scheme by finite element method and discuss its convergence. At last, the given numerical examples adequately confirm the correctness of theoretical analysis and compare the computing effectiveness between the fast algorithm and the direct method. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the nonlinear fractional pseudo‐parabolic equations (FPPEs). We propose an accurate numerical algorithm for solving the aforementioned well‐known equation. The problem is discretized in the temporal direction by utilizing a graded mesh linearized scheme and in the spatial direction by the Galerkin‐spectral scheme. We investigate the stability conditions of the proposed scheme. We also provide an H1$$ {H}^1 $$ error estimate of the proposed approach to demonstrate that it is convergent with temporal second‐order accuracy for fitted grading parameters. The proposed scheme is also extended to tackle coupled FPPEs. Numerical experiments are provided to validate the accuracy and reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a new real representation of reduced biquaternion matrix is proposed, and the solutions of the reduced biquaternion matrix equations XF−AX=BY$$ XF- AX= BY $$ and XF−AX˜=BY$$ XF-A\tilde{X}= BY $$ are solved by means of this method. The corresponding numerical algorithm is provided, and the effectiveness of this method is verified by numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical algorithm dealing with multi‐term time‐fractional Burgers‐type equation involving the Caputo derivative. The proposed method consists of temporal discretization of L2$$ L2 $$ formula and spatial discretization using the exponential B‐splines. The semi implicit approach is applied to discretize the nonlinear term u∂xu$$ u{\partial}_{\mathtt{x}}u $$. We adopt the Von–Neumann method to study stability. We also establish the convergence analysis. The proposed method is employed to solve a few numerical examples in order to test its efficiency and accuracy. Comparisons with the recent works confirm the efficiency and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Probabilistic record linkage is the act of bringing together records that are believed to belong to the same unit (e.g., person or business) from two or more files. It is a common way to enhance dimensions such as time and breadth or depth of detail. Probabilistic record linkage is not an error‐free process and link records that do not belong to the same unit. Naively treating such a linked file as if it is linked without errors can lead to biased inferences. This paper develops a method of making inference with estimating equations when records are linked using algorithms that are widely used in practice. Previous methods for dealing with this problem cannot accommodate such linking algorithms. This paper develops a parametric bootstrap approach to inference in which each bootstrap replicate involves applying the said linking algorithm. This paper demonstrates the effectiveness of the method in simulations and in real applications. [ABSTRACT FROM AUTHOR]

The most common approach to solving blade element momentum (BEM) equations is through fixed point method. The fixed point method can provide reliable solutions with high precision, yet the robustness of the method has been challenged when infrequent failures of converging to a physical solution are found for some design space. Though the lack of robustness is alleviated by applying two improved algorithms, their shortcomings should not be of an understatement. Ning's method can result in a converged yet nonphysical solution, and Sun's method decreases the computational efficiency remarkably. To overcome these setbacks, a new algorithm has been proposed in this paper. A clear classification of a wind turbine operating states has been given first to correct the thrust relation for a > 1, followed by discussions of three failure cases encountered during solving BEM equations. Then, the new algorithm with three major modifications has been introduced and explained. The test of Section 4 reveals that the decreasing rf technique has a positive effect on improving the robustness. Besides, the first two tests in Section 5 prove that the new thrust equation can greatly enhance the robustness, and Aitken's squared process can significantly strengthen the efficiency. The results show that all three modifications contribute to offering a new FPA with high robustness and satisfactory computing efficiency, which serves as the best option for solving the BEM equations. [ABSTRACT FROM AUTHOR]

The monodomain model is widely used in in‐silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi‐implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting‐based methods. [ABSTRACT FROM AUTHOR]

Comparing with the classic phase filed models, the fractional models such as time fractional Allen–Cahn and Cahn–Hilliard equations are equipped with Caputo fractional derivative and can describe more practical phenomena for modeling phase transitions. In this paper, we construct two accurate and efficient linear algorithms for the time fractional Cahn–Hilliard and Allen–Cahn equations with general nonlinear bulk potential. The main contribution is that we have proved the unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn models and their semi‐discrete schemes carefully and rigorously. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of our proposed schemes. [ABSTRACT FROM AUTHOR]

The solution of a system of linear equations is very important in various fields of engineering, and various methods have been presented for the numerical solution. Especially, in the adaptive signal processing and adaptive control, the system of equations is often considered where the coefficient matrix is (pseudo-) positive-definite and symmetrical. The conjugate graduate method is known as a means to solve such a system of equations. Letting the rank of the coefficient matrix be R, it is a method where the solution for the system of equations is determined by iterating a certain procedure R times. In this method, even if the iterative process is terminated on the way due to the constraint for the computation time, for example, an approximate solution which is somewhat accurate is obtained. This method, however, still has room for improvement with respect to the accuracy of the approximate solution. From such a viewpoint, this paper examines geo- metrically the iterative computation process in the con- jugate gradient method and, based on that result, propos- es a new method of iterative solution for the system of linear equations with symmetrical coefficient matrix. Then the original method is slightly modified and an adaptive algorithm is derived by applying the result to the parameter estimation of the adaptive filter. Those methods are based on the orthogonal projection operation from the solution to be determined to the linear space. Consequently, it is expected that, even if the iterative computation is terminated on the way, a more accurate approximate solution is obtained, compared to the case of the conjugate gradient method or the adaptive algorithm based on the conjugate gradient method. By the property of the method proposed in this paper, the method is useful when the coefficient matrix is ill-conditioned. It is expected that the method will effectively be utilized in the signal processing and control. [ABSTRACT FROM AUTHOR]

In this paper, we employ three integration algorithms, namely, the well‐known Kudryashov method, the new Kudryashov method, and the unified Riccati equation expansion method to extract optical soliton solutions for the generalized Kudryashov equation with power nonlinearities. Straddled soliton, bright solitons, dark solitons, and singular solitons have been found. [ABSTRACT FROM AUTHOR]

Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ⊂ ℝ3 with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H1(Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions. [ABSTRACT FROM AUTHOR]

In this paper, we find the solution and analyse the behaviour of the obtained results for the nonlinear Schrödinger‐Boussinesq equations using q‐homotopy analysis transform method (q‐HATM) within the frame of fractional order. The considered system describes the interfaces between intermediate long and short waves. The projected fractional operator is proposed with the help of Mittag‐Leffler function to incorporate the nonsingular kernel to the system. The projected algorithm is a modified and accurate method with the help of Laplace transform. The convergence analysis is presented with the help of the fixed point theorem in the form existence and uniqueness. To validate and illustrate the effectiveness of the algorithm considered, we exemplified considered system with respect of arbitrary order. Further, the behaviour of achieved results is captured in contour and 3D plots for distinct arbitrary order. The results show that the projected scheme is very effective, highly methodical and easy to apply for complex and nonlinear systems and help us to captured associated behaviour diverse classes of the phenomenon. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm based on a sequence of three modified Newton procedures to solve the constrained minimization problem. In the literature, numerical integration rules for the tetrahedron are available up to order p=15. We obtain integration rules for the tetrahedron from p=2 to p=20, which are computed using multiprecision arithmetic. For p≤15, our approach provides integration rules that have the same or fewer number of integration points than existing rules; for p=16 to p=20, our rules are new. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, rational, weakly singular and trigonometric test functions over tetrahedra with flat and curved faces. In all tests, improvements in accuracy is realized as p is increased, though in some cases nonmonotonic convergence is observed. [ABSTRACT FROM AUTHOR]

Multiple imputation by chained equations (MICE) has emerged as a leading strategy for imputing missing epidemiological data due to its ease of implementation and ability to maintain unbiased effect estimates and valid inference. Within the MICE algorithm, imputation can be performed using a variety of parametric or nonparametric methods. Literature has suggested that nonparametric tree-based imputation methods outperform parametric methods in terms of bias and coverage when there are interactions or other nonlinear effects among the variables. However, these studies fail to provide a fair comparison as they do not follow the well-established recommendation that any effects in the final analysis model (including interactions) should be included in the parametric imputation model. We show via simulation that properly incorporating interactions in the parametric imputation model leads to much better performance. In fact, correctly specified parametric imputation and tree-based random forest imputation perform similarly when estimating the interaction effect. Parametric imputation leads to slightly higher coverage for the interaction effect, but it has wider confidence intervals than random forest imputation and requires correct specification of the imputation model. Epidemiologists should take care in specifying MICE imputation models, and this paper assists in that task by providing a fair comparison of parametric and tree-based imputation in MICE. [ABSTRACT FROM AUTHOR]

The problem of finding the point in time at which a known audio or video source (reference signal) appears in a long audio or video source (input signal) is referred to as a time series search, in contrast to a text string search. In a time series search, a search can be performed quickly by combining the audio and video, and then identifying several search conditions using logical equations. Thus, in this paper the authors describe the application of the time series active search method, a method to search audio signals proposed in the authors' previous paper, to video searches. Next, the authors propose an efficient algorithm for AND searches and OR searches of reference signals. In addition, the authors propose a multimodal AND search which combines audio and video. The proposed algorithms are faster than combining the results of searches performed individually. For instance, in an OR search of a reference signal, when the mutual similarity in the reference signals is above 0.8, five reference signals can be searched in a search time that is 1.2 times faster than searching one reference signal. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(12): 54–64, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10142 [ABSTRACT FROM AUTHOR]

This paper considers theoretically the relation between the convergence problem of various algorithms and statistical properties of a signal appearing during construction of a linear prediction system of signals when the tine series of the signal is a multiple Gaussian process. Specifically, we consider first the convergence problem of the covariance matrix of a predicted error arising as a linear prediction algorithm applied to the solution of a Yuleswalker equation. Next, in comparison with the convergence speed of the correlation coefficient matrix of a multiple signal time series, we obtain an evaluation formula for the convergence speed of a covariance matrix of a linear prediction error. Furthermore, we discuss the convergence of an algorithm for constructing an orthonormalized polynomial matrix which corresponds to a transfer function matrix of a whitening filter from a solution of the Yule-Walker equation. We present a concrete evaluation formula for the convergence speed of the algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes an iterative approximation technique of log-magnitude response for IIR filters. Minimization of the mean-square error between a desired log-frequency response and that of an IIR filter leads to a nonlinear problem. In this paper, the least squares problem on the logarithmic scale is approximated by the iteration of a weighted least squares problem on the linear scale. The weighting function is updated using the result of the previous iteration so that the weighted error on the linear scale approximates the squared error on the logarithmic scale. The filter coefficients at each iteration step can efficiently be obtained using a fast recursive algorithm for a set of linear equations. Several design examples are presented, which show that the iterative algorithm converges after one or two iterations in practice and the weighted error at convergence gives a good, estimate of the mean-square error on the logarithmic scale. An example is also presented, where both log-magnitude and phase responses are approximated simultaneously. [ABSTRACT FROM AUTHOR]

The article presents the response of Abou El-Makarim Aboueissa to the comments made by Igor Kovasev about his paper describing a proposed algorithm to approximate the maximum likelihood estimates (MLE) equations using a computer algorithm. He offers some clarifications about a new computer algorithm for obtaining the Cohen's MLE which does not require auxiliary tables. He argues that equations 12 and 13 as explained in the paper are equal.

SUMMARY Bootstrap algebraic multigrid (BAMG) is a multigrid-based solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0. This paper studies an improved form of BAMG, called relaxation-corrected bootstrap algebraic multigrid ( rBAMG), that involves adding scaled residuals of the test vectors to the least-squares equations. The basic rBAMG scheme was introduced in an earlier paper [1] and analyzed on a simple model problem. The purpose of the current paper is to further develop this algorithm by incorporating several new critical components and to systematically study its performance on an interesting model problem from quantum chromodynamics. Whereas the earlier paper introduced a new least-squares principle involving the residuals of the test vectors, a simple extrapolation scheme is developed here to accurately estimate the convergence factors of the evolving algebraic multigrid solver. Such a capability is essential to the effective development of a fast solver, and the approach introduced here is shown numerically to be much more effective than the conventional approach of just observing successive error reduction factors. Another component of the setup process developed here is an adaptive cycling process. This component assesses the effectiveness of the V-cycle constructed in the initial rBAMG phase by applying it to the homogeneous equation. When poor convergence is observed, the set of test vectors is enhanced with the resulting error, enabling the subsequent least-squares fit of interpolation to produce an improved V-cycle. A related component is the scaling and recombination Ritz process that targets the so-called weak approximation property in an attempt to reveal the important elements of these evolving error and test vector spaces. The aim of the numerical study documented here is to provide insight into the various design choices that arise in the development of an rBAMG algorithm. With this in mind, the results for quantum chromodynamics focus on the behavior of rBAMG in terms of the number of initial test vectors used, the number of relaxation sweeps applied to them, and the size of the target matrices. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as-rigid-as-possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre-aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closest-point search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general-purpose non-linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Within system dynamics, optimization has played an important role in identifying the best range of parameter values for policies in any given model. Optimal solutions focus on discovering the best combination of model parameters, within a fixed policy equation structure, that maximize or minimize a payoff function. This paper presents a new optimization approach for system dynamics. It enables decision makers to vary policy equation structures during the optimization process. The resulting optimization approach—based on genetic algorithms—can explore the search space in order to discover the best combination of parameters and equation-based strategies for a given system dynamics problem. The approach is best suited to the class of system dynamics problems that are agent-based, and the work is evaluated using a case study based on the four-agent beer game. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently, efficient algorithms have been proposed for finding all solutions of nonlinear equations using linear programming (LP). These algorithms are based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the LP test, a system of nonlinear equations is transformed into an LP problem by surrounding component nonlinear functions by rectangles or right-angled triangles. In this paper, an efficient algorithm is proposed for finding all solutions of weakly nonlinear equations, where component nonlinear functions are surrounded by parallelograms and then the dual simplex method is applied to the LP problem. Numerical examples are given to confirm the effectiveness of the proposed algorithm. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(7): 1–7, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20220 [ABSTRACT FROM AUTHOR]

The minimal principle for structure determination from single-crystal X-ray diffraction measurements has recently been formulated as an integer linear optimization model for the case of centrosymmetric structures. Solution of this model via established combinatorial branch-and-bound algorithms provides the true global minimum of the minimal principle while operating exclusively in reciprocal space. However, integer programming techniques may require an exponential number of iterations to exhaust the search space. In this paper, a new approach is developed to solve the integer minimal principle to global optimality without requiring the solution of an optimization problem. Instead, properties of the solution of the optimization problem, as observed in a large number of computational experiments, are exploited in order to reduce the optimization formulation to a system of linear equations in the number field of two elements (F2). Two specialized Gaussian elimination algorithms are then developed to solve this system of equations in polynomial time in the number of atoms. Computational results on a collection of 38 structures demonstrate that the proposed approach provides very fast and accurate solutions to the phase problem for centrosymmetric structures. This approach also provided much better crystallographic R values than SHELXS for all 38 structures tested. [ABSTRACT FROM AUTHOR]

In this paper, simple modifications to the pseudospectral time-domain (PSTD) algorithm that offer dispersion compensation are presented. In a homogeneous lossless medium, the compensation offers an exact solution for one-dimensional (1D) propagation. For 2D and 3D propagation, the proposed method can compensate dispersion for a central frequency in any direction. The techniques are then extended to inhomogeneous materials containing piecewise constant electromagnetic properties and are shown to offer dispersion compensation. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 357–361, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20304 [ABSTRACT FROM AUTHOR]

In this paper, the traffic performance of dynamic channel assignment (DCA) in cellular mobile system with hand-off is investigated. A traffic model for cellular system incorporating hand-off is established first. Under the framework of the model, a hand-off priority scheme is developed to reduce the forced termination of calls in progress. This paper analyses and derives the traffic performance bound for DCA strategies with hand-off by extending the maximum packing (MP) scheme to include the hand-off procedure. For practical implementation, a distributed DCA algorithm (DDCA) is also proposed. A non-priority scheme and the proposed priority scheme can be combined with either MP or DDCA. It is shown that the simulation results of DDCA scheme are comparable with the analytical bounds given by MP for both the non-prioritized case and prioritized case. A reasonable trade-off between the new call blocking probability and forced termination probability can be achieved by using the proposed prioritized scheme in DCA. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When a region with a certain area needs silencing, no sufficient effect can be obtained with a single-channel active noise control system. Therefore, multiple channel noise control systems using several microphones and speakers have been proposed. One of the algorithms used frequently is the Multiple Error Filtered-X (MEFX) method. The MEFX method requires prior estimation of the error path system. In the case of multiple channels, the estimation error poses more complex effects in comparison to the single channel. In addition, variations of the system during operation are problematic. In this paper, the simultaneous equation method recently proposed for the single channel in which no estimation is required for the error path system is applied to the multiple channel active noise control. In the present procedure, the coefficients of the noise control filter can be estimated without estimation of the error path system as in the case of the single channel. The method can handle the variation of the path during operation and can obtain excellent silencing effects. © 2002 Scripta Technica, Electron Comm Jpn Pt 3, 85(5): 46–55, 2002 [ABSTRACT FROM AUTHOR]

Half-band filters are a class of important filters among digital filters, and have been widely used in many applications such as filter banks and wavelets. The conventional methods are mainly concerned with FIR half-band filters with exactly linear phase. However, the exactly linear phase filters have a drawback of large group delay when high-order filters are required. In this paper, the design of FIR half-band filters with a lower group delay is considered. In some applications of filter banks and wavelets, a flat magnitude response is required for the half-band filters. Therefore, a new method for designing low-delay FIR half-band filters with arbitrary flatness is proposed. In the proposed method, while taking the specified flatness condition into account, the design problem is formulated by using the complex Remez exchange algorithm in the stopband. Then, a set of filter coefficients can be easily obtained by solving a simple system of linear equations. The optimal solution with an equiripple response in the stopband is obtained by applying an iteration process. Finally, the proposed method is applied to the design of two-channel perfect reconstruction filter banks with low group delay to demonstrate its effectiveness. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(10): 1–9, 2000 [ABSTRACT FROM AUTHOR]

This paper is a comparative analysis of two prominent iterative algorithms for model order reduction of linear time‐varying (LTV) periodic systems where the system's matrices are singular. Our proposed method is based on a reformulation of the LTV model to an equivalent linear time‐invariant (LTI) model using a suitable discretization procedure. The resulting LTI model is reduced in two ways, once by applying a balanced truncation method and once by applying a Krylov‐based method known as iterative rational Krylov algorithm (IRKA). During the application of balanced truncation, the low‐rank Cholesky factorized alternating directions implicit (LRCF‐ADI) method is used to estimate the solutions of the corresponding LTI form of Lyapunov equations. Since the system's matrices are singular, the concept of pseudo‐inverse is adopted to compute the shift parameters needed in the LRCF‐ADI iterations. For the Krylov‐based IRKA, our work is twofold. We solve the time‐invariant Lyapunov equation for the observability Gramian and apply a moment‐matching Krylov technique. The accuracy and effectiveness of the two proposed techniques are demonstrated with the help of frequency response graphs, bode plots, and eigenstructure of the main and reduced models. [ABSTRACT FROM AUTHOR]

In this paper a parallel algorithm is created for solving electromagnetic wave scattering problems. The algorithm based on the finite difference time-domain (FDTD) representation of the Maxwell's equations written in 3L Parallel Fortran for use on a transputer array. The problem simulated consists of a space (air) where a spherical dielectric scatterer is located. This space is subdivided into fine equisize meshes extending throughout the 3-D domain; the excitation wave is of sinusoidal form. Geometric decomposition is used as the principal algorithm strategy. Results are presented for the performance of the classical sequential algorithm and compared with the parallel algorithm in terms of computational speed-up. [ABSTRACT FROM AUTHOR]

Forecasts are routinely revised, and these revisions are often the subject of informal analysis and discussion. This paper argues (1) that forecast revisions are analyzed because they help forecasters and forecast users to evaluate forecasts and forecasting procedures and (2) that these analyses can be sharpened by using the forecasting model to systematically express its forecast revision as the sum of components identified with specific subsets of new information, such as data revisions and forecast errors. An algorithm for this purpose is explained and illustrated. [ABSTRACT FROM AUTHOR]

This paper considers the case where the block-state realization is applied to state-space digital filters and discusses the synthesis method for the minimum coefficient sensitivity realization. First, the method to evaluate the coefficient sensitivity in the block-state realization, which has already been reported by the authors, is shown. Thai the synthesis method for the minimum coefficient sensitivity realization is presented based on the evaluation method for the cases with and without the scaling constraint. It is shown as a result that the minimum coefficient sensitivity realization can be derived as a balanced structure also in the block-state realization, as in the usual state-space realization. Finally, calculation examples are shown for those synthesis methods and the validity of the proposed synthesis method is demonstrated by the satisfactory results. It is shown also that the minimum coefficient sensitivity structure for the block-state realization derived by the proposed synthesis method is equivalent to the filter structure in the block-state realization, which is derived from the minimum coefficient sensitivity structure in the usual state-space realization. [ABSTRACT FROM AUTHOR]

The integer labeling method is one of the simplicial-type homotopy methods for solving systems of nonlinear equations. In this method, matrix operations are not necessary and an approximate solution can be generated only by function evaluations. Thus, the algorithm becomes quite simple and can easily be programmed. However, since the integer labeling method uses simplicial subdivision, the amount of computations grows exponentially with the system size. For the vector labeling method, which is another type of homotopy methods, an efficient algorithm using a rectangular subdivision has been proposed. For the integer labeling method, however, such an efficient technique has not been proposed because integer labeling on rectangles is essentially impossible. This paper proposes an efficient integer labeling method for solving systems of nonlinear equations with separable mappings. Similarly to the conventional method, the proposed method labels integers on simplices. However, by making use of the separability and the concept of the rectangular subdivision, the number of function evaluations is reduced significantly. In the proposed method, function evaluations are not necessary as long as the labeled simplex is moving in the identical rectangle, and when it moves into another rectangle, only one component of the function in that direction needs to be computed. Hence, with the increase of the system size, considerable improvements of the computational efficiency can be achieved. [ABSTRACT FROM AUTHOR]

Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified Riemann-Liouville derivative has been described and demonstrated. The algorithm has been tested against time-fractional differential-difference equations of rational type via symbolic computation. Three examples are given to elucidate the solution procedure. Our analyses lead to closed form exact solutions in terms of hyperbolic, trigonometric, and rational functions, which might be subject to some adequate physical interpretations in the future. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this work, an explicit family of time marching procedures with adaptive dissipation control is introduced. The proposed technique is conditionally stable, second-order accurate, and has controllable algorithm dissipation, which adapts according to the properties of the governing system of equations. Thus, spurious modes can be more effectively dissipated and accuracy is improved. Because this is an explicit time integration technique, the new family is quite efficient, requiring no system of equations to be dealt with at each time step. Moreover, the technique is simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed method, as well as its potentialities. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, high‐order numerical methods for time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations in one‐ and two‐dimensional space are constructed, where the second‐order backward fractional difference operator and the sixth‐order fractional‐compact difference operator are applied to approximate the time and space fractional derivatives, respectively. The stability and convergence of the methods are analyzed and it is shown that the convergence orders are higher than the earlier work. Finally, some numerical experiments are presented to demonstrate the effectiveness of the methods and confirm our theoretical results. [ABSTRACT FROM AUTHOR]

SUMMARY This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three-dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a reformulation of the original Matsuoka-Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non-associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, on the basis of the D'Alembert's principle, approximate formulas for dynamic response of tubular tall building structures are presented. Using D'Alembert's principle and applying the compatibility conditions on deformation of the tubes, the governing dynamic equation of the tubular structure's motion is derived. Then, natural boundary conditions of the parallel cantilevered flexural-shear beams are derived, and by using Rayleigh-Ritz method, value problem is solved, and trivial and nontrivial solutions are derived, which can be used for calculating natural frequencies and mode shapes of tubular structures. By solving numerically the frequency equation, a design chart and graph are given for the first five nondimensional natural frequencies of tubular tall buildings. The proposed mathematical model gives dynamic characteristics and provides a simple, efficient and reasonably accurate algorithm for free vibration studies that are needed to be quick at the preliminary design stages of tall buildings with tubular systems. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The numerical solution of D-bar integral equations is the key in inverse scattering solution of many complex problems in science and engineering including conductivity imaging. Recently, a couple of methodologies were considered for the numerical solution of D-bar integral equation, namely product integrals and multigrid. The first one involves high computational complexity and other one has low convergence rate disadvantages. In this paper, a new and efficient sinc-convolution algorithm is introduced to solve the two-dimensional D-bar integral equation to overcome both of these disadvantages and to resolve the singularity problem not tackled before effectively. The method of sinc-convolution is based on using collocation to replace multidimensional convolution-form integrals- including the two-dimensional D-bar integral equations - by a system of algebraic equations. Separation of variables in the proposed method allows elimination of the formulation of the huge full matrices and therefore reduces the computational complexity drastically. In addition, the sinc-convolution method converges exponentially with a convergence rate of [ABSTRACT FROM AUTHOR]

The partitioning of colour differences into Δ L*, Δ C* and Δ H* is not directly equivalent to the dyer's method of partitioning. The dyer's method involves separation into the components of depth (Δ D), brightness (Δ B) and hue (Δ H), of which only hue difference has a qualitative (and quantitative) equivalent in the CIELAB system. Depth and brightness are important terms to dyers. Depth is related to the amount of dye taken up by a textile material and brightness to that component of colour difference that is neither depth nor hue. Brightness is best defined as the opposite of dullness, dullness being related to the amount of neutral grey present in the colour. An algorithm, called the Wardman-Smith-Farooq algorithm, has been developed to compute the dyers' variables of Δ D,Δ B and Δ H from spectral reflectance values, enabling dyers to take full advantage of colorimetry. The algorithm is based on extensive experimental work to map surfaces of constant visual depth through the colour space and this paper describes the methodology of the calculation. The correlations of the values of Δ D,Δ B and Δ H, determined using the Wardman-Smith-Farooq algorithm with other empirical models for 117 sample pairs, are given. [ABSTRACT FROM AUTHOR]

The least mean squares (LMS) algorithm, the most commonly used channel estimation and equalization technique, converges very slowly. The convergence rate of the LMS algorithm is quite sensitive to the adjustment of the step-size parameter used in the update equation. Therefore, many studies have concentrated on adjusting the step-size parameter in order to improve the training speed and accuracy of the LMS algorithm. A novel approach in adjusting the step size of the LMS algorithm using the channel output autocorrelation (COA) has been proposed for application to unknown channel estimation or equalization in low-SNR in this paper. Computer simulations have been performed to illustrate the performance of the proposed method in frequency selective Rayleigh fading channels. The obtained simulation results using HIPERLAN/1 standard have demonstrated that the proposed variable step size LMS (VSS-LMS) algorithm has considerably better performance than conventional LMS, recursive least squares (RLS), normalized LMS (N-LMS) and the other VSS-LMS algorithms. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is very important to maintain supply reliability in the deregulated environment. The transient stability problem is one of the major concerns in studies of planning and operation of power systems. Time domain simulation is currently the best available tool for allowing the use of detailed models and for providing reliable results. The main limitations of this approach involve long computation times. Therefore, this paper proposes a transient stability evaluation method using minimum transient kinetic energy of postfault trajectories. This method can estimate critical clearing times with only two points of the minimum transient kinetic energy, regardless of whether the trajectories after the clearing time are stable or unstable. The validity of the proposed method is shown by simulation studies with the IEEJ EAST 10-machine 47-bus system. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 174(3): 18-24, 2011; Published online in Wiley Online Library (). DOI 10.1002/eej.21018 [ABSTRACT FROM AUTHOR]

A system of ℓ linear equations in p unknowns Mx = b is said to have the removal property if every set S ⊆ {1, …, n} that contains o(np−ℓ) solutions of Mx = b can be turned into a set S′ containing no solution of Mx = b by the removal of o(n) elements. Green (Geom. Funct. Anal. 15 (2005) 340–376) proved that a single homogenous linear equation always has the removal property, and conjectured that every set of homogenous linear equations has the removal property. In this paper we confirm Green's conjecture by showing that every set of linear equations (even non-homogenous) has the removal property. We also discuss some applications of our result in theoretical computer science and, in particular, use it to resolve a conjecture of Bhattacharyya, Chen, Sudan and Xie related to algorithms for testing properties of boolean functions. [ABSTRACT FROM PUBLISHER]

This paper presents the design of a power system stabilizer using decentralized adaptive model following tracking control (DAMFTC) approach to damp oscillations of generators in transient response subjected to uncertainties and generating fault actuators. The power system is represented as a collection of interconnected dynamical subsystems each described by a set of differential/algebraic equations using a clear representation of load voltage magnitude with matched and unmatched time-varying uncertainties. All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis subject to state errors due to uncertainties and fault section, so that stability and robustness of the closed-loop system are ensured and asymptotic-state tracking can be achieved. An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertainties. The effectiveness of the proposed approach is demonstrated by distributing a detailed simulation of the three-machine nine-bus system with nonlinear interactions, uncertainties, and fault actuators. The simulation includes the effects of network and stator transients. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents some variants of the inexact Newton method for solving systems of nonlinear equations defined by locally Lipschitzian functions. These methods use variants of Newton's iteration in association with Krylov subspace methods for solving the Jacobian linear systems. Global convergence of the proposed algorithms is established under a nonmonotonic backtracking strategy. The local convergence based on the assumptions of semismoothness and BD-regularity at the solution is characterized, and the way to choose an inexact forcing sequence that preserves the rapid convergence of the proposed methods is also indicated. Numerical examples are given to show the practical viability of these approaches. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

DiffServ architecture has been widely adopted for the provision of QoS over the Internet. This makes the full understanding of its operation imperative. We believe that only mathematical analysis may have the power of such goal. As the heart of a DiffServ router is the token bucket algorithm, a generic one, with two-colours marking, is to be considered here. A mathematical framework will be first developed for its analysis. Then, assuming an input traffic with Poisson arrivals and Exponential packet lengths, and a memoryless token bucket system, the two types of generated streams will be statistically characterized through their distributions and averages. This analysis will be carried out for two types of buckets, one with infinite size and a second with finite size. It will be shown how the derived equations will allow the prediction of the output traffic streams for given bucket and input traffic stream parameters. The paper will be then complemented by conclusions and suggestions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper gives a procedure for evaluating the Fisher information matrix for a general multiplicative seasonal autoregressive moving average time-series model. The method is based on the well-known integral specification of Whittle [ Ark. Mat. Fys. Astr. (1953) vol. 2. pp. 423–434] and leads to a system of linear equations, which is independent of the seasonal period and has a closed solution. It is shown to be much simpler, in general, than the method of Klein and Mélard [ Journal of Time Series Analysis (1990) vol. 11, pp. 231–237], which depends on the seasonal period. It is also shown that the nonseasonal method of McLeod [ Biometrika (1984) vol. 71, pp. 207–211] has the same basic features as that of Klein and Mélard. Explicit solutions are obtained for the simpler nonseasonal and seasonal models in common use, a feature which has not been attempted with the Klein–Mélard or the McLeod approaches. Several illustrations of these results are discussed in detail. [ABSTRACT FROM AUTHOR]

The solution of large sparse linear systems of equations is one of the cornerstones of scientific computation. In many applications it is important to be able to solve these systems as rapidly as possible. One approach for very large problems is to reorder the system matrix to bordered block diagonal form and then to solve the block system using a coarse-grained parallel approach. In this paper, we consider the problem of efficiently ordering unsymmetric systems to singly bordered block diagonal form. Algorithms such as the MONET algorithm of Hu et al. (Comput. Chem. Eng. 23 (2000) 1631) that depend upon computing a representation of AAT can be prohibitively expensive when a single (or small number of) matrix factorizations are required. We therefore work with the graph of AT + A (or BT + B, where B is a row permutation of A) and propose new reordering algorithms that use only vertex separators and wide separators of this graph. Numerical experiments demonstrate that our methods are efficient and can produce bordered forms that are competitive with those obtained using MONET. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the microstrip circuit is analyzed in terms of the mixed potential integral equation (MPIE) by using the rooftop-function expansion and the blaze-function testing technique. The integral equation is solved by the inner-outer flexible generalized minimal residual fast Fourier transform (FGMRES-FFT) method. Our numerical calculations show that the FGMRES-FFT method can converge as high as five times faster than the generalized minimal residual-fast Fourier transform (GMRES-FFT) method and 16 times faster than the conjugate gradient-fast Fourier transform (CG-FFT) method. Some typical microstrip discontinuities are analyzed and the good results obtained demonstrate the validity of the proposed algorithm. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 409–413, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20485 [ABSTRACT FROM AUTHOR]