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This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}^2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

The simulation of slowly varying electromagnetic fields is possible for very large, realistic problems with finite-difference implicit time-domain (FDiTD) and frequency-domain (FDFD) formulations on the basis of the consistent Finite-Integration Technique (FIT). Magneto-quasistatic time-domain formulations combined with implicit time marching schemes require the repeated solution of real-valued symmetric systems. The solution of driven frequency domain problems usually consists in the solution of one non-Hermitean system. Preconditioned conjugate gradient-type methods are well-suited for this task. They allow the efficient solution even for consistent singular or near-singular systems, which typically arise from formulations for slowly varying electromagnetic fields using the Maxwell-Grid-Equations of the FI-Method. Numerical results for TEAM workshop 11 benchmark problem and for a large practical problem, a shading ring sensor, show that the presented algorithms are capable of solving realistic problems for large numbers of unknowns in acceptable calculation times on contemporary medium sized workstations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The delay time concept is widely adopted in literature to model the two‐stage failure process of most industrial systems which can be divided into normal stage (from new to an initial point of a defect) and defective stage (from defect arrival point to failure). Most existing delay time models assume that the normal and defective stages are independent. A generalized delay time model is proposed in this paper by considering the dependence between the normal and defective stages which is reflected in the fact that they share the same external shock process. According to the definition of shot‐noise process, external shocks will incur random hazard rate increments in the two stages. The failure state is self‐announcing, whereas the defective state can only be detected by block‐based inspection or opportunistic inspection offered by unexpected shutdown due to unavoidable external factors. The system is correctively replaced upon the occurrence of a system failure or preventively replaced at the detection of a defective state. Based on the stochastic failure model and maintenance policy, this paper evaluates system reliability performance and average long‐run cost rate via a Markov‐chain based approach. Finally, a case study on a steel convertor plant is given to demonstrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effect of adding a coarse mesh correction to the two‐grid algorithm for the mixed Navier–Stokes/Darcy model. The method yields both L2 and H1 optimal velocity and piezometric head approximations and an L2 optimal pressure approximation. The method involves solving one small, coupled, nonlinear coarse mesh problem, two independent subproblems (linear Navier–Stokes equation and Darcy equation) on the fine mesh, and a correction problem on the coarse mesh. Theoretical analysis and numerical tests are done to indicate the significance of this method. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references. [ABSTRACT FROM AUTHOR]

Summary: This paper studies a low‐communication algorithm for solving elliptic PDEs on high‐performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers. [ABSTRACT FROM AUTHOR]

This paper presents an MLP-type neural network with some fixed connections and a backpropagation-type training algorithm that identifies the full set of solutions of a complete system of nonlinear algebraic equations with n equations and n unknowns. The proposed structure is based on a backpropagation-type algorithm with bias units in output neurons layer. Its novelty and innovation with respect to similar structures is the use of the hyperbolic tangent output function associated with an interesting feature, the use of adaptive learning rate for the neurons of the second hidden layer, a feature that adds a high degree of flexibility and parameter tuning during the network training stage. The paper presents the theoretical aspects for this approach as well as a set of experimental results that justify the necessity of such an architecture and evaluate its performance. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

With the increasing complexity of engineering systems, reliability analysis and evaluation of systems with traditional methods can't meet practical engineering requirements. Based on limited experimental conditions, lack of data, complex structure models, insufficient cognitive abilities, and many other issues, people have to consider many uncertain factors in system reliability research. Besides, common cause failure (CCF) has become an important factor of system failure. In this paper, a discrete‐time Bayesian network (DTBN) associated with an eight‐rotor unmanned aerial vehicle (UAV) system is presented to discuss above problems. In this approach, the system is assumed as a two‐state system. After that, interval analysis theory is employed to deal with uncertainty. We consider the four sets of auxiliary propellers in the auxiliary power group as a 3/8 voting system, and β factor model is used to process CCF in the auxiliary power group. The proposed methods prove the validity of proposing interval analysis theory to solve uncertain problems and it is necessary to consider reducing or avoiding CCFs in system. [ABSTRACT FROM AUTHOR]

Since Compton cameras were introduced in the use of single photon emission computed tomography, various types of conical Radon transforms, which integrate the emission distribution over circular cones, have been studied. Most of previous works did not address the attenuation factor, which may lead to significant degradation of image quality. In this paper, we consider the problem of recovering an unknown function from conical projections affected by a known constant attenuation coefficient called an attenuated conical Radon transform. In the case of a fixed opening angle and vertical central axis, new explicit inversion formula is derived. Two‐dimensional numerical simulations were performed to demonstrate the efficiency of the suggested algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF. [ABSTRACT FROM AUTHOR]

Summary: Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem. [ABSTRACT FROM AUTHOR]

This paper presents feedback sensitivity functions analysis of implicit Lyapunov function-based control system in case of finite-time stabilization problem. The Gang of Four is chosen as a feedback sensitivity tool. The results can be used for parametric tuning of control algorithms in order to guarantee desired closed-loop sensitivity specifications. The obtained results are supported by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The contour integral-based eigensolvers are the recent efforts for computing the eigenvalues inside a given region in the complex plane. The best-known members are the Sakurai-Sugiura method, its stable version CIRR, and the FEAST algorithm. An attractive computational advantage of these methods is that they are easily parallelizable. The FEAST algorithm was developed for the generalized Hermitian eigenvalue problems. It is stable and accurate. However, it may fail when applied to non-Hermitian problems. Recently, a dual subspace FEAST algorithm was proposed to extend the FEAST algorithm to non-Hermitian problems. In this paper, we instead use the oblique projection technique to extend FEAST to the non-Hermitian problems. Our approach can be summarized as follows: (a) construct a particular contour integral to form a search subspace containing the desired eigenspace and (b) use the oblique projection technique to extract desired eigenpairs with appropriately chosen test subspace. The related mathematical framework is established. Comparing to the dual subspace FEAST algorithm, we can save the computational cost roughly by a half if only the eigenvalues or the eigenvalues together with their right eigenvectors are needed. We also address some implementation issues such as how to choose a suitable starting matrix and design-efficient stopping criteria. Numerical experiments are provided to illustrate that our method is stable and efficient. [ABSTRACT FROM AUTHOR]

Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such high-performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems. This paper is a self contained state-of-the-art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research. [ABSTRACT FROM AUTHOR]

The paper proposes a stress-driven integration strategy for Perzyna-type viscoplastic constitutive models, which leads also to a convenient algorithm for viscoplastic relaxation schemes. A generalized trapezoidal rule for the strain increment, combined with a linearized form of the yield function and flow rules, leads to a plasticity-like compliance operator that can be explicitly inverted to give an algorithmic tangent stiffness tensor also denoted as the m-AGC tangent operator. This operator is combined with the stress-prescribed integration scheme, to obtain a natural error indicator that can be used as a convergence criterion of the intra-step iterations (in physical viscoplasticity), or to a variable time-step size in viscoplastic relaxation schemes based on a single linear calculation per time step. The proposed schemes have been implemented for an existing zero-thickness interface constitutive model. Some numerical application examples are presented to illustrate the advantages of the new schemes proposed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a propagator matrix method applied to logging-while-drilling tools is introduced and extended to deal with the anisotropic and radially inhomogeneous earth formations. This method expands the Maxwell's equations in the transverse direction, constructs the relationship between propagator matrix and reflection matrix, and obtains the solution by using the reflection matrix. We systematically derived the formulas of propagator matrix method in isotropic media, uniaxially anisotropic media, fully anisotropic media, and radially inhomogeneous media respectively. In order to obtain the propagator matrix in complex media, we used the fourth-order Runge-Kutta scheme. Numerical experiments show that, compared with traditional methods, the propagator matrix method has wide range of applications while maintaining low computational costs and high accuracy. All algorithms presented in the paper have been parallelized and implemented on a high-performance computing platform. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This special issue contains a selection of papers from the Sixth International Workshop on the Numerical Solution of Markov Chains, held in Williamsburg, Virginia on September 16-17, 2010. The papers cover a broad range of topics including perturbation theory for absorbing chains, bounding techniques, steady-state and transient solution methods, multilevel algorithms, preconditioning, and applications. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY For a Markov reward process, where upper and lower bounds for the transition rates and rewards are known, a new approach to bound the expected reward is presented. Based on a previous paper where sharp bounds have been defined for the problem, but only an inefficient and unstable algorithm is proposed, this paper presents algorithms to compute the bounds by interpreting the problem as a Markov Decision Process. In this way, the well known value and policy iteration algorithms can be adopted to compute reward bounds in a stable and fairly efficient way. Different numerical techniques are presented for computing the reward bounds. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

With the aid of the finite element method, a lot of mechanical and thermal phenomena in forming processes can be analysed successfully. However, for industrial purposes the necessary computational time for complex processes is often not acceptable. Many researches have attempted to reduce the computational time which is needed to find a solution. In this paper, new algorithms are described which make use of the existing similarity in some forming processes, especially incremental forming process. Incremental forming processes are characterised by very small deformation zones and approximate self similarity. The described algorithms are based on the transformation and interpolation of already computed solutions. The results from transformation and interpolation are verified by means of some physical constraints. If the results pass the latter check, they will be archived as solution. Consequently, at this time step, no iterative computation will be accomplished by the mechanical solver. Then the calculations by the thermo solver are accomplished conventionally in dependence on the archived mechanical results. With the help of these algorithms, the number of iterations will obviously be reduced and the results will be reasonably acceptable. In this paper, all details are described and two forming processes as validation occur to depict the advantages of this method. [ABSTRACT FROM AUTHOR]

This paper presents a simple approach to determine the time-step size required in the alternate-direction-implicit finite-difference time-domain (ADI-FDTD) method in order to obtain a desired numerical dispersion accuracy. The Courant number, the desired dispersion accuracy, and the maximum mesh size Δmax = max(Δx, Δy, Δz) are governed by the numerical dispersion relation, which can be solved by a simple root-finding algorithm to evaluate the Courant number and hence the time-step size for a given mesh size and accuracy. The time-step size is independent of the aspect ratio. To determine if ADI-FDTD is more efficient than the Yee's FDTD, this paper provides a simple relation to evaluate the relative Courant–Friedrich–Levy number (CFLN) from the Courant number and the aspect ratio. The ADI-FDTD method is more efficient than Yee's FDTD when the aspect ratio is high or the mesh density is very large. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 487–490, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20012 [ABSTRACT FROM AUTHOR]

Helmholtz equations with variable coefficients are known to be hard to solve both analytically and numerically. In this paper, we introduce a numerical multigrid solver for one-dimensional Helmholtz eigenvalue problems with periodic potentials and solutions. The solvers employ wave–ray methodology suggested by Brandt, Livshits for Helmholtz equations with constant coefficients. The paper concludes with numerical experiments and the discussion of future efforts for solving two-dimensional problems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In optimal design of a permanent magnet (PM) motor, many design variables are required to consider some device properties. These variables are, for example, the shape of core and magnet, the tooth length, the number of turns, and the winding radius. Moreover, many restrictions must be considered in practical PM motor design. These restrictions are, for example, the slot space factor and the cogging torque. However, the optimization problem, which has many design variables by the finite element method (FEM), has not been reported. In this paper, the efficiency of PM motor under the considerations given above is optimized by using FEM and optimization algorithm. In this problem, an objective function has many local minima and it is difficult to calculate its gradient. For these reasons, the genetic algorithm (GA) and simulated annealing method (SA), which are stochastic methods, are used for optimization method, because of the possibility of global range search and because gradient calculation is not required. Adding to both optimization methods, in this paper, SA combined with GA is used for one of the optimization methods. It is found that the solutions optimized by these methods are reasonable from an engineering point of view. © 2001 Scripta Technica, Electr Eng Jpn, 138(3): 72–79, 2002 [ABSTRACT FROM AUTHOR]

In this paper an efficient algorithm is presented for the development of compact and passive macro-models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of finite elements. The proposed methodology is founded on a new finite element formulation that casts Maxwell's curl equations in a state-space form. Such state-space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the finite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation efficiency can be avoided by a proper selection of the finite element expansion functions used for the discretization of the electromagnetic fields. More specifically, it is shown that the proper selection of expansion functions renders the state-space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector finite elements. This equivalence is then used to effect Krylov-based model order reduction directly from the finite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macro-modelling algorithm is demonstrated through its application to a variety of microwave passive components. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present a far-field pattern calculation technique in the body-of-revolution finite-difference time-domain (BOR–FDTD) method. Because the BOR–FDTD solves two- and half-dimensional problems, it has different features from the three-dimensional FDTD method in the far-field pattern calculation. A monopole antenna fed by a coax is used to validate the technique described in this paper. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 47–50, 2001. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyze a BDDC algorithm for a class of elliptic problems in the three-dimensional H( curl) space. Compared with existing results, our condition number estimate requires fewer assumptions and also involves two fewer powers of log( H/h), making it consistent with optimal estimates for other elliptic problems. Here, H/h is the maximum of H i/ h i over all subdomains, where H i and h i are the diameter and the smallest element diameter for the subdomain Ω i. The analysis makes use of two recent developments. The first is a new approach to averaging across the subdomain interfaces, while the second is a new technical tool that allows arguments involving trace classes to be avoided. Numerical examples are presented to confirm the theory and demonstrate the importance of the new averaging approach in certain cases. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is one of the partial differential equations appearing in a number of research areas including mathematics, physics, engineering, and biology. Its applicable area is quite wide. In this paper, as a solution method for an NLSE accompanied with modification or perturbation (generalized NLSE), the - integral method (NM) is used. The basic concept, formulation, and actual numerical calculation algorithm are described. The NM introduced by Feynman is a nonrelativistic quantum mechanical formulation based on the Lagrangian font Since the final formula obtained in this paper takes a standard Fourier transform type, it is possible to use the fast Fourier transform (FFT) so that a quantum jump in numerical efficiency has been attained. it should be noted that only one Fourier transform operation is needed per unit propagating section. As a generalized NLSE, a set of coupled nonlinear Schrödinger equations with a perturbation is considered. As a specific example of application, numerical results for optical solitons are presented. [ABSTRACT FROM AUTHOR]

This paper presents a method of numerical analysis by the multiple input describing function for the self-excited oscillation in a nonlinear system with hysteresis. In the traditional analysis by the describing function, the decribing function for the hysteresis is determined in an analytic form, and a very complex calculation is required to perform a highly accurate analysis including the harmonic components of the self-excited oscillation. Consequently, in practice, it has been impossible to determine analytically the describing function for the multiple input. Furthermore, the calculation is impossible for the describing function, where the hysteresis characteristics contain a minor loop. From such a viewpoint, this paper proposes a method and algorithm for the analysis of self-excited oscillation. In the proposed method, the describing function is determined numerically by the digital simulation of the hysteresis, and the discrete Fourier transform and its inverse are applied to the result. But this method, the describing function can be determined numerically even for the cases of multiple input and the case with a minor loop. Thus, the self-excited oscillation can be analyzed considering the harmonic components and the multiple mode. As an example, the self-excited oscillation of the nonlinear system is analyzed for the case where the linear part is represented by a second-order transfer function or by a sum of such functions. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

The information storage algorithm of a Hopfield-type network is a kind of self-correlation learning. This algorithm needs the condition in which vectors of learning patterns cross at right angles to each other. This paper proposes n method to make this condition easier. To this purpose, threshold is used. An investigation of how to decide quantity is included. This paper discusses a network with units whose state is 1 or 0. Fixing method of threshold has not been proposed before to this type of network. It is, therefore, proposed in this research; the goal is to facilitate learning patterns. [ABSTRACT FROM AUTHOR]

This paper proposes a design method for the FIR two-channel perfect quadrature mirror filter (QMF) with the linear phase. The two-channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics. This paper presents the design for the two-channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude charac- teristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations. The construction of the two-channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two-dimensional (2-D) perfect QMF is designed by applying the McClellan transformation to the obtained 1-D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived. [ABSTRACT FROM AUTHOR]

This paper shows that the learning identification (the normalized LMS) algorithm can be expressed by a first-order IIR lowpass filter having rapidly varying coefficients as a function of output signal to be sent to an unknown system to be estimated. Based on the expression, this paper studies the estimation error of adaptive filters obtained by the learning identification algorithm. It is pointed out that the mean of estimation error given by the conventional analysis corresponds to the output fluctuation which can be computed by replacing varying coefficients of the lowpass filter with its arithmetic mean. However, the output fluctuation is affected by the time constant specified by the coefficients of the lowpass filter and it has a characteristic that it increases rapidly when time constant is short and decreases slowly when it is long. This means that the actual estimation error becomes larger than the result given by the conventional analysis. According to the analysis shown in this paper, it can be seen that the estimation error consists of elements for which the portion increased by the effect of time constant become fewer anti-proportionally to the number of the tap, and those elements which increase at a constant rate independently of the number of the tap. It was shown also by simulation using white noise that the difference between the estimation error obtained in actual estimation operation which occurs when the number of the tap is small and the result given by the conventional analysis can be explained well by the analysis by simulation using white noise. [ABSTRACT FROM AUTHOR]

Recently, for signal processing such as echo cancellation and equalization it is required to develop IIR-adaptive digital filters. This paper proposes a new-type IIR- adaptive algorithm based on the orthogonalization method, considers the convergence of the algorithm, and verifies its effectiveness by simulation. White's algorithm is one of IIR-adaptive algorithms reported thus far and Feintuch's algorithm is known as its approximation algorithm. This paper also derives an IIR-adaptive algorithm using both Feintuch's algorithm and the orthogonalization method, First, it can be shown that a generalized algorithm (IIR-LI) of IIR-learning identification method based on previous heuristic methods can be derived using the idea of Feintuch's algorithm and the conjugate gradient method. Next, a new IIR-adaptive algorithm (IIR-AACG) based on the orthogonalization principle of the conjugate gradient method is presented. Further, by applying the orthogonalization method to a past input vector sequence we derive an IIR-Affine projection algorithm (1IR-AP). Finally, these algorithms are compared by computer simulation to verify the effectiveness of the orthogonalization method. [ABSTRACT FROM AUTHOR]

gggggAssume that an n × n dot matrix is stored in consecutive n words of a computer with one word being n bit. This paper discusses eight operations to rotate or transpose the dot matrix in horizontal/vertical! slant direction. As is well known, such operations form a group. This paper presents a unified description of the algorithms, and it is shown that all eight algorithms can be derived by suit- ably setting the constants in the unified algorithm. Then it is shown that the algorithms can be transformed to each other by simple transformation rules for the constants, and those transformation rules are shown to form a group. The foregoing algorithms for the dot matrix are not unique, and there can be different descriptions for the algorithm producing the same result. Consequently, there can be various versions of the eight algorithms as well as versions of transformation rules. This paper shows that one of the two groups formed by the transformation rules is isomorphic to the group of algorithms, but the other is not isomorphic. [ABSTRACT FROM AUTHOR]

In this paper, a numerical analysis algorithm has been derived for the analysis of the problem of plane wave diffraction by a multilayered grating. This algorithm is based on the Yasuura method with the smoothing procedure and can be applied to the problems of arbitrary multilayered dielectric (or metallic) grating with smoothly shaped grooves. The convergence of the approximate solution obtained by the present algorithm has been investigated numerically. It was demonstrated that a highly accurate approximate solution can be computed by the introduction of the smoothing procedure. The present algorithm is applicable to problems of a multilayered grating over the range from infrared to visible. As a numerical example, the diffraction efficiency of the multilayered diffraction grating made of alternate lamination of the high-index and low-index dielectric layers deposited on a metal grating is calculated by the algorithm in this paper. The following items are confirmed: (1) by coating dielectric films, the power absorption of the incident light by the metal grating is reduced in a specific wavelength region; and (2) in a multilayered grating, anomalous resonant absorption occurs by the coupling of the guided mode excited by the dielectric thin film and the diffracted wave. [ABSTRACT FROM AUTHOR]

This paper presents the dispersion characteristics of the FD-TD algorithm by showing the numerical phase and group velocities of the TEM, TE or TM modal solutions. For the TEM wave propagation, there exist three fundamental directions to which phase and group velocities can be expressed by only a single variable (wave number k or frequency ω). Those special directions were chosen to show the dispersive nature of the FD-TD algorithm of which the group and phase velocities depend explicitly on frequencies. In view of similarities between the TLM and FD-TD algorithms, a comparison of phase velocity characteristics of both methods was made. Under the special condition where the stability factor s is larger than ½, the FD-TD algorithm is found less dispersive than that of the original TLM. However, newly developed symmetrical TLM method appears less dispersive than the FD-TD algorithm. In the numerical simulation of waveguide modal solutions, it was found that there exists an optimum frequency which provide least numerical error in the FD-TD application. A procedure, which determines the stability factor s and the maximum allowed frequency Fmax for the best numerical results, is proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient algorithm for finding all solutions of nonlinear resistive circuits. As a computational method of finding all solutions of nonlinear equations, interval analysis is well known, and the Krawczyk algorithm is one of the most typical algorithms of interval analysis. However, the Krawcyzk algorithm is extremely inefficient for circuit equations whose nonlinearity is very great. In this paper, several techniques are proposed for improving the computational efficiency of the Krawczyk algorithm for circuit equations. These techniques exploit the special structure of the circuit equations such as separability or partial linearity. It is shown that the computation time of the Krawczyk algorithm is substantially decreased by using the proposed techniques. © 1997 Scripta Technica, Inc Electron Comm Jpn Pt 3, 80(7): 28–36, 1997 [ABSTRACT FROM AUTHOR]

Hammocks have been considered by Brenner [1], who gave a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck [11] gave a combinatorial definition of left hammocks which generalised the concept of hammocks in the sense of Brenner, as a translation quiver H and an additive function h on H (called the hammock function) satisfying some conditions. They showed that a thin left hammock with finitely many projective vertices is just the preprojective component of the Auslander-Reiten quiver of the category of 5-spaces, where 5 is a finite partially ordered set (abbreviated as 'poset'). An important role in the representation theory of posets is played by two differentiation algorithms. One of the algorithms was developed by Nazarova and Roiter [8], and it reduces a poset 5 with a maximal element a to a new poset 52=a-5. The second algorithm was developed by Zavadskij [13], and it reduces a poset 5 with a suitable pair (a, b) of elements a, b to a new poset 52=(a,b)5. The main purpose of this paper is to construct new left hammocks from a given one, and to show the relationship between these new left hammocks and the Nazarova-Roiter algorithm. In a later paper [5], we discuss the relationship between hammocks and the Zavadskij algorithm. [ABSTRACT FROM AUTHOR]

As a method of solving the electromagnetic scattering by perfectly conducting cylinders, the discrete singularity method is discussed. For this method, a finite number of singular points is distributed within the scatterer and the wave function composed of a linear combination of solutions (each of which is derived from a helmholtz equation with each single singularity among the many) is matched with the incident wave function on the boundary. The remaining important problem in this method is how to distributed these singularities in order to obtain the accurate solution with faster convergence and with fewer number of singular points for an arbitrary configuration of the scatterer. The purpose of this paper is to present a reasonable solution to this problem. The essential of the method is that by making as unknown quantities, not only the unknown amplitude coefficients involved in the linear combination of the solutions, but also the coordinates of the singularities, the scattered wave is matched on the boundary in the sense of the least squares. This problem is linear in the amplitude coefficient but nonlinear in the singularity coordinate. Thus we solve this problem by using the algorithm by marquardt et al, of a nonlinear optimization process. This paper considers the general description and indicates its effectiveness by showing a few examples of the scattering problem of rectangular cylinders. [ABSTRACT FROM AUTHOR]

In this paper, the problem of power allocation in a cooperative cognitive radio (CR) network is investigated. An optimal power allocation is proposed to maximize efficiency of the secondary network in which secondary users transmit simultaneously over a spectral band assigned to the primary users. The CR network employs directional relays to improve efficiency of the communication links and minimize interference introduced to the primary users. Unlike the conventional cooperative relay-assisted network, the directional relays are grouped in clusters. This clustering technique along with directional transmission can significantly reduce interference to the primary links and improve the system performance. Two algorithms are also developed on the basis of the penalty method to determine unknown transmission powers. Some corroborant numerical examples are provided to illustrate quick convergence behavior of the proposed algorithms and great superiority of employing clustered directional relays in cooperative CR networks. [ABSTRACT FROM AUTHOR]

SUMMARY The paper offers an algorithm for local and global parametric diagnosis in nonlinear analog circuits, including both identification of the faulty parameters and determination their values. The algorithm exploits a nonlinear algebraic type test equations which may possess multiple solutions, corresponding to different sets of the parameters values which meet the test. To find the solutions, the homotopy concept is applied. Since the test equation is not given in explicit analytical form, the simplicial method is used to trace the homotopy path. The proposed approach can be applied to a broad class of analog circuits, including the complementary metal-oxide-semiconductor circuits fabricated in nanometer technology. The developed diagnostic procedure has been implemented in DELPHI, whereas the required by the algorithm repeated circuit analyses are carried out using IsSPICE 4 and both environments have been joined together. For illustration, two numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding minimum-norm fixed point of nonexpansive mappings. We present two types of iteration methods (one is implicit, and the other is explicit). We establish strong convergence theorems for both methods. Some applications are given regarding convex optimization problems and split feasibility problems. These results improve some known results existing in the literatures. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a new alternating direction implicit (ADI) method is introduced to solve potential driven geometric flow PDEs for biomolecular surface generation. For such PDEs, an extra factor is usually added to stabilize the explicit time integration. However, two existing implicit ADI schemes are also based on the scaled form, which involves nonlinear cross derivative terms that have to be evaluated explicitly. This affects the stability and accuracy of these ADI schemes. To overcome these difficulties, we propose a new ADI algorithm based on the unscaled form so that cross derivatives are not involved. Central finite differences are employed to discretize the nonhomogenous diffusion process of the geometric flow. The proposed ADI algorithm is validated through benchmark examples with analytical solutions, reference solutions, or literature results. Moreover, quantitative indicators of a biomolecular surface, including surface area, surface-enclosed volume, and solvation free energy, are analyzed for various proteins. The proposed ADI method is found to be unconditionally stable and more accurate than the existing ADI schemes in all tests. This enables the use of a large time increment in the steady state simulation so that the proposed ADI algorithm is very efficient for biomolecular surface generation. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper aims to present a general framework of the quadratic spline functions to develop a numerical method for solving the nonlinear space fractional Fisher's equation. Using Von Neumann method, the proposed method is shown to be conditionally stable. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. The results reveal that the proposed approach is very effective, convenient, and quite accurate to such considered problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Optimal design problems for semiconductor devices with relevant thermal effects can be formulated by help of the energy transport model. In this paper we perform a sensitivity analysis to derive the first-order necessary condition for the optimization. Exploiting the special structure of the KKT system we use a special variant of the classical Gummel iteration to provide a very fast optimization algorithm. Numerical results for a ballistic diode underline the feasibility of our approach. [ABSTRACT FROM AUTHOR]

SUMMARY An iterative method for finding the largest eigenvalue of a nonnegative tensor was proposed by Ng, Qi, and Zhou in 2009. In this paper, we establish an explicit linear convergence rate of the Ng-Qi-Zhou method for essentially positive tensors. Numerical results are given to demonstrate linear convergence of the Ng-Qi-Zhou algorithm for essentially positive tensors. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Absrtact Discovering temporal patterns hidden in a sequence of events has applications in numerous areas like network failure analysis, customer behaviour analysis, web navigation pattern discovery, etc. In this article, we present an approach to the discovery of chronicles hidden in the interaction traces of a human activity with the intention of characterizing some interesting tasks. Chronicles are a special type of temporal patterns, where temporal orders of events are quantified with numerical bounds. The algorithm we present is the first existing chronicle discovery algorithm that is complete. It is a chronicle discovery framework that can be configured to behave exactly as non-complete algorithms existing in litterature with no reduction of performance, but it can also be extended to other useful chronicle discovery problems like hybrid episode discovery. We show that the complete chronicle discovery problem has a very high complexity but we argue and illustrate that this high complexity is acceptable when the knowledge discovery process in which our algorithm takes part is real time and interactive. The platform Scheme Emerger, also presented in this paper, has been developed in order to implement the algorithm and to support graphically the real time and interactive chronicle discovery process. [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]

This paper presents an automatic process for fabrication-oriented design of custom-shaped rubber balloons. We cast computational balloon design as an inverse problem: given a target shape, we compute an optimal balloon that, when inflated, approximates the target as closely as possible. To solve this problem numerically, we propose a novel physics-driven shape optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm. We validate our approach by fabricating balloons designed with our method and comparing their inflated shapes to the results predicted by simulation. An extensive set of manufactured sample balloons demonstrates the shape diversity that can be achieved by our method. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a practical two-term acceleration algorithm is proposed, the interval of the parameter which guarantees the convergence of the acceleration algorithm is analyzed in detail. Further, the acceleration ratio of the new acceleration algorithm is obtained in advance. The new acceleration algorithm is less sensitive to the parameter than the Chebyshev semi-iterative method. Finally, some numerical examples show that the accelerated algorithm is effective. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]