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The reference signals used in a multichannel system are usually strongly crosscorrelated. Preprocessing is normally added to reduce the crosscorrelation between the reference signals because this correlation makes estimating the adaptive filter coefficients difficult. However, this preprocessing is equivalent to warping the reference signals. The transmission of these warped reference signals to an unknown system hinders the essential system operation. On the other hand, it is necessary for uncorrelated components between the reference signals to exist when estimating the adaptive filter coefficients. Preprocessing that increases the ratio of these components is important in improving the convergence characteristics. In this paper, we propose an algorithm that does not transmit preprocessed reference signals to an unknown system, but only uses them to estimate the adaptive filter coefficients, and explain the design conditions needed to implement this algorithm. In other words, with the condition of not increasing the estimation errors, we derive the optimum values of the coefficients that reduce the correlation between the reference signals, which is a feature of this algorithm, and verify its effectiveness in simulations. By employing the proposed algorithm, improvements in the convergence characteristics can be designed without affecting the essential operation of the system. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(3): 32–41, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20092 [ABSTRACT FROM AUTHOR]

Summary: This paper presents some recent advances for parallel‐in‐time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel‐in‐time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel‐in‐time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF‐relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel‐in‐time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. The paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely, the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty‐type regularisation of discrete operators and the LaTIn hybrid‐mixed formulation of complex interface conditions. Furthermore, the novel P1‐P1 discretisation scheme that we propose for the unfitted LaTIn solver is shown to be stable, robust, and optimally convergent with mesh refinement. Finally, the paper introduces a high‐performance 3D level set/CutFEM framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries, with more than 2 bodies interacting at a single point. [ABSTRACT FROM AUTHOR]

An adaptive chaos particle swarm optimization (ACPSO) is presented in this paper to tune the parameters of proportional-integral-derivative (PID) controller. To avoid the local minima, we introduced a constriction factor. Meanwhile, the chaotic searching is combined with the particle swarm optimization to improve the ability of the proposed algorithm. A series of experiment is performed on 6 benchmark functions to confirm its performance. It is found that the ACPSO can get better solution quality in solving the global optimization problems and avoiding the premature convergence. Based on it, the proposed algorithm is applied to tune the PID controller's parameters. The performances of the ACPSO are compared with different inspired algorithms, and these results show that the ACPSO is more robust and efficient when it is used to find the optimal parameters of PID controller. [ABSTRACT FROM AUTHOR]

This paper addresses the job-shop scheduling problem to minimize total waiting time. This also is equivalent to minimizing the work in process. Although, this problem is of relevance to manufacturing systems (Job-shops), most of the work in the literature concerns the minimization of makespan for which the algorithms proposed are implicit enumeration procedures. For the minimization of total waiting time, to our knowledge, there are only empirical priority rules, all of which construct non-delay schedules (i.e. there is no inserted idle time on the machines). In this work, we use theoretical results obtained for a single machine scheduling problem to construct an efficient heuristic for the problem at hand. This algorithm provides active schedules that are not always non-delay schedules. The convergence and the complexity of the algorithm are discussed. The performance is also evaluated with respect to a classical priority rule. [ABSTRACT FROM AUTHOR]

Based on the extended extragradient-like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz-type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Our work is devoted to an inverse problem for three-dimensional parabolic partial differential equations. When the surface temperature data are given, the problem of reconstructing the heat flux and the source term is investigated. There are two main contributions of this paper. First, an adjoint problem approach is used for analysis of the Fréchet gradient of the cost functional. Second, an improved conjugate gradient method is proposed to solve this problem. Based on Lipschitz continuity of the gradient, the convergence analysis of the conjugate gradient algorithm is studied. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new channel assignment strategy named compact dynamic channel assignment (CDCA) is proposed. The CDCA differs from other strategies by consistently keeping the system in the utmost optimal state, and thus the scheme allows to determine a call succeeding or failing by local information instead of that of the whole network. It employs Hopfield neural networks for optimization which avoids the complicated assessment of channel compactness and guarantees optimum solutions for every assignment. A scheme based on Hopfield neural network is considered before; however, unlike others, in this algorithm an energy function is derived in such a way that for a neuron, the more a channel is currently being allocated in other cells, the more excitation the neuron will acquire, so as to guarantee each cluster using channels as few as possible. Performance measures in terms of the blocking probability, convergence rate and convergence time are obtained to assess the viability of the proposed scheme. Results presented show that the approach significantly reduces stringent requirements of searching space and convergence time. The algorithm is simple and straightforward, hence the efficient algorithm makes the real-time implementation of channel assignment based on neural network feasibility. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new algorithm for the unconstrained optimization problem, which is derived as an application of the control theory called Direct Gradient Descent Control. The static optimization problem is solved by using a dynamic controller in which the convergence speed can be greatly accelerated. The major idea is to consider the objective function F(x) and its time derivative dF(x(t))/dt as the evaluation criteria, and to apply the gradient descent method. It is verified by simulation that the proposed dynamic mathematical programming has a very great capability to converge to the optimal solution. It is also interesting to note that the method has to a certain extent the ability to find not only local optimal solutions, but also global optimal solutions. This paper improves the basic algorithm of dynamic mathematical programming so that it is suited to global optimization. The new algorithm generates movement toward the global optimal solution by utilizing two different trajectories with interaction (the chaotic trajectory and convergence trajectory). It is verified by simulation that the new algorithm functions as a global optimization procedure with a high success probability. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(6): 20–27, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20094 [ABSTRACT FROM AUTHOR]

Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which have an optimal order computational complexity with respect to the size of the system. Such methods were first presented in Axelsson and Padiy (SIAM. J. Sci. Stat. Comp. 1990; 20:1807) and Axelsson and Vassilevski (Numer. Math. 1989; 56:157), and are based on (recursive) two-level splittings of the finite element space. The key role in the derivation of optimal convergence rate estimates is played by the constant γ in the so-called Cauchy–Bunyakowski–Schwarz (CBS) inequality, associated with the angle between the two subspaces of the splitting. It turns out that only existence of uniform estimates for this constant is not enough but accurate quantitative bounds for γ have to be found as well. More precisely, the value of the upper bound for γ∈(0,1) is part of the construction of various multilevel extensions of the related two-level methods. In this paper, an algebraic two-level preconditioning algorithm for second-order elliptic boundary value problems is constructed, where the discretization is done using Crouzeix–Raviart non-conforming linear finite elements on triangles. An important point to make is that in this case the finite element spaces corresponding to two successive levels of mesh refinements are not nested. To handle this, a proper two-level basis is considered, which enables us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. The major contribution of this paper is the derived estimates of the related constant γ in the strengthened CBS inequality. These estimates are uniform with respect to both coefficient and mesh anisotropy. To our knowledge, the results presented in the paper are the first such estimates for non-conforming FEM systems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

It is known in the normalized least mean square (NLMS) algorithm that the convergence time can be reduced by applying a control in which the step gain is gradually reduced, as the estimation precision is improved. A problem in realizing this idea is that the instantaneous value of the estimation precision which is needed in the control of the step gain cannot be observed directly from the residual signal which contains external disturbances. This paper considers a block length control, which can be used in the “summational” NLMS method. The method is able to improve the convergence of the estimation precision, as in step gain control, and a method of reducing the convergence time is proposed, utilizing the fact that saturation of the convergence behavior can be observed iteratively by extending the block. In addition, it is highly likely in an actual adaptive system that the reference signal, the power of the external disturbance, and the impulse response of the unknown system to be estimated as the coefficients of the finite impulse response (FIR) filter will change. It is not realistic to ignore the possibility of these changes in discussing the control of convergence. In the last part of this paper, it is shown that the proposed control method can handle these changes. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(12): 54–64, 1999 [ABSTRACT FROM AUTHOR]

In this paper, the geometric learning algorithm (GLA) is proposed for an elementary perceptron which includes a single output neuron. The GLA is a modified version of the affine projection algorithm (APA) for adaptive filters. The weight update vector is determined geometrically with respect to the orthogonal complement of the k patterns to be classified, where k is the order of the GLA. In the case of the APA, the target of the coefficient update is a single point which corresponds to the best identification of the unknown system. On the other hand, in the case of the GLA, the target of the weight update is the area in which all of the given patterns are classified correctly. Thus, their convergence conditions are different. In this paper, the convergence condition of the first-order GLA for 2 patterns is derived theoretically. The condition is represented by the relation between the angle θ of 2 patterns and the learning rate λ. Next, the new concept of the angle ψmin of the solution area is introduced for the case of many patterns. Computer simulation results indicate that the relation between ψmin and λ for convergence can be approximated by the relation between θ and λ for 2 patterns. Furthermore, it is proved that the first-order GLA always converges regardless of the number of patterns when λ = 2. By our analysis and proof, the convergence of the first-order GLA is guaranteed and its usefulness as the learning algorithm is confirmed. The distributions of ψmin and λ for the convergence of the first-order GLA are approximately determined. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(9): 29–38, 1999 [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]

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]

Reproducing kernel Hilbert space method is given for nonlinear boundary‐value problems in this paper. Applying this technique, we establish a new algorithm to approximate the solution of such nonlinear boundary‐value problems. This technique does not need any background mesh and can easily be applied. In this technique, the solution is given in the form of a series. Representation of the solutions is obtained in the reproducing kernel Hilbert space. Additionally, the convergence of the presented method is demonstrated. Numerical examples are presented to show the ability of the method. We compare the reproducing kernel Hilbert space method with B‐spline collocation method. As seen in the tables, the reproducing kernel Hilbert space method gives better results. [ABSTRACT FROM AUTHOR]

SUMMARY In a recent paper an algorithm for large-scale Tikhonov regularization in standard form called GKB-FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided, and extensions to general-form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method coupled with an automatic stopping rule is proposed. Preconditioning seeks to incorporate smoothing properties of the regularization matrix into the computed solution. Numerical results are reported to illustrate the methods on large-scale problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high-order method possesses eighth-order convergence. The interesting point is that, this rate is attained using less number of matrix-by-matrix multiplications in contrast to the existing methods of the same type in the literature. The extension of the method for finding Moore-Penrose inverse of singular or rectangular matrices is also presented. Numerical comparisons will be given to show the applicability, stability and consistency of the new scheme by paying special attention on the computational time. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Convergence property of the iterative algorithm for Hammerstein or Wiener systems is generally hard to establish because of the existence the unmeasurable internal variables in such systems. In this paper, a fixed-point iteration is introduced to identifying both Hammerstein and Wiener systems with a unified algorithm. This newly proposed estimation algorithm gives consistent estimates under arbitrary nonzero initial conditions. In addition, the errors of the estimates are established as functions of the noise variance, and thus how the noise affects the quality of parameter estimates for a finite number of data points is made clear. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the full discrete scheme of mixed finite element approximation is introduced for semilinear hyperbolic equations. To solve the nonlinear problem efficiently, two two‐grid algorithms are developed and analyzed. In this approach, the nonlinear system is solved on a coarse mesh with width H, and the linear system is solved on a fine mesh with width h≪H. Error estimates and convergence results of two‐grid method are derived in detail. It is shown that if we choose H = O ( h 1 3 ) in the first algorithm and H = O ( h 1 4 ) in the second algorithm, the two‐grid algorithms can achieve the same accuracy of the mixed finite element solutions. Finally, the numerical examples also show that the two‐grid method is much more efficient than solving the nonlinear mixed finite element system directly. [ABSTRACT FROM AUTHOR]

In this paper, a novel high-order optimal terminal iterative learning control (high-order OTILC) is proposed via a data-driven approach for nonlinear discrete-time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high-order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high-order OTILC to outperform the low-order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is data-driven in which no explicit models are used except for the input and output data. The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed-batch fermentater demonstrate the effectiveness of the proposed high-order OTILC design. [ABSTRACT FROM AUTHOR]

Nonlinear complementarity problem (NCP) is a wide class of problems. In this paper, some two-level additive Schwarz algorithms for NCPs with an M-function are developed and analyzed. The algorithms are proved to be convergent monotonically and can reach the solution of the problem within finite steps. They may also offer a possibility of making use of fast nonlinear solvers for solving the subproblems involved in the algorithms. Some preliminary numerical results are reported. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Some computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo-inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore-Penrose pseudo-inverse computation have been tested for modal analysis of a four-flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well-known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and fl is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. [ABSTRACT FROM AUTHOR]

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low-level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. The Gauss–Seidel method is used as a smoother, and a linear equation of lowest level is solved by the ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algorithm of constant term using a null space of the coefficient matrix is also described. In three-dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the conventional ICCG method. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(1): 39–45, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10228 [ABSTRACT FROM AUTHOR]

In this paper, we use recent results of Jarner & Roberts ( Ann. Appl. Probab., 12, 2002, 224) to show polynomial convergence rates of Monte Carlo Markov Chain algorithms with polynomial target distributions, in particular random-walk Metropolis algorithms, Langevin algorithms and independence samplers. We also use similar methodology to consider polynomial convergence of the Gibbs sampler on a constrained state space. The main result for the random-walk Metropolis algorithm is that heavy-tailed proposal distributions lead to higher rates of convergence and thus to qualitatively better algorithms as measured, for instance, by the existence of central limit theorems for higher moments. Thus, the paper gives for the first time a theoretical justification for the common belief that heavy-tailed proposal distributions improve convergence in the context of random-walk Metropolis algorithms. Similar results are shown to hold for Langevin algorithms and the independence sampler, while results for the mixing of Gibbs samplers on uniform distributions on constrained spaces are rather different in character. [ABSTRACT FROM AUTHOR]

This paper analyses a novel method for constructing preconditioners for diagonally dominant symmetric positive-definite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal non-zeros from A and modifying the diagonal elements to maintain a certain row-sum property. The preconditioners are extensions of Vaidya's augmented maximum-spanning-tree preconditioners. The preconditioners presented here were also mentioned by Vaidya in an unpublished manuscript, but without a complete analysis. The preconditioners that we present have only O(n+t2) nonzeros, where n is the dimension of the matrix and 1⩽t⩽n is a parameter that one can choose. Their construction is efficient and guarantees that the condition number of the preconditioned system is O(n2/t2) if the number of nonzeros per row in the matrix is bounded by a constant. We have developed an efficient algorithm to construct these preconditioners and we have implemented it. We used our implementation to solve a simple model problem; we show the combinatorial structure of the preconditioners and we present encouraging convergence results. [ABSTRACT FROM AUTHOR]

Gene clustering, the process of grouping related genes in the same cluster, is at the foundation of different genomic studies that aim at analyzing the function of genes. Microarray technologies have made it possible to measure gene expression levels for thousands of genes simultaneously. For knowledge to be extracted from the datasets generated by these technologies, the datasets have to be presented to a scientist in a meaningful way. Gene clustering methods serve this purpose. In this paper, a hybrid clustering approach that is based on self-organizing maps and particle swarm optimization is proposed. In the proposed algorithm, the rate of convergence is improved by adding a conscience factor to the self-organizing maps algorithm. The robustness of the result is measured by using a resampling technique. The algorithm is implemented on a cluster of workstations. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep neural networks, it essentially relies on obtaining the unbiased estimates of gradients/subgradients of the objective functions. In this paper, by constructing the randomised differences of the objective function, a gradient‐free algorithm, named the stochastic randomised‐difference descent algorithm, is proposed for stochastic convex optimisation. Under the strongly convex assumption of the objective function, it is proved that the estimates generated from stochastic randomised‐difference descent converge to the optimal value with probability one, and the convergence rates of both the mean square error of estimates and the regret functions are established. Finally, some numerical examples are prsented. [ABSTRACT FROM AUTHOR]

In this paper, we study cutting plane methods for a Lagrangian relaxation-based unit commitment algorithm. In the algorithm, nondifferentiable optimization methods can be applied to optimize the dual function, and a subgradient method which needs parameter tuning and has some drawbacks such as computational inefficiency and oscillating behavior is commonly used. The cutting plane method and the central cutting plane method are applied to the algorithm and implemented using reoptimization techniques. A numerical example shows that both methods are accelerated by the reoptimization techniques and have good convergence without parameter tuning. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(3): 17–29, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10066 [ABSTRACT FROM AUTHOR]

Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l2 norm, however, the optimal convergence result is available only in the energy norm (or the equivalent Sobolev H1 norm). Very little progress has been made in the theoretical understanding of the l2 behaviour of this very successful algorithm. To add to the difficulty in developing a full l2 theory, in this note, we construct explicit examples and show that the optimal convergence of additive Schwarz preconditioned GMRES in l2 cannot be obtained using the existing GMRES theory. More precisely speaking, we show that the symmetric part of the preconditioned matrix, which plays a role in the Eisenstat–Elman–Schultz theory, has at least one negative eigenvalue, and we show that the condition number of the best possible eigenmatrix that diagonalizes the preconditioned matrix, key to the Saad–Schultz theory, is bounded from both above and below by constants multiplied by h-1/2. Here h is the finite element mesh size. The results presented in this paper are mostly negative, but we believe that the techniques used in our proofs may have wide applications in the further development of the l2 convergence theory and in other areas of domain decomposition methods. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an efficient solution for solving the generalized eigenvalue equation arising in the finite-element (FE) formulation of propagation characterization of planar transmission-line structures. A two-dimensional (2-D) finite-element method (FEM) is used for analyzing the uniform planar transmission lines. The Arnoldi algorithm is used in conjunction with the multifrontal decomposition of the system matrix for solving the eigensystem. Convergence is typically obtained within a few iterations of the Arnoldi process, and the formulation has proven to be robust, even when dealing with a significantly large number of unknowns. Numerical results are presented for the case of a uniform microstrip line, which clearly show the computational savings resulting from the use of the present approach. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 194–197, 2001. [ABSTRACT FROM AUTHOR]

In this paper, we study a modified normalized least mean square (NLMS) algorithm for updating coefficients of an adaptive FIR digital filter (ADF). In the modified adaptive algorithm, filter coefficients are updated with the NLMS algorithm for each sample, but the coefficients are frozen when the input signal is smaller than a given threshold (constant). This modified NLMS has been known, but not been analyzed. In this paper, we call the modified NLMS the “conditioned NLMS” (C-NLMS) and analyze the convergence characteristics. As a result, the optimum threshold value is obtained. The simulation results and theoretical analyses show the effectiveness of the C-NLMS with the proposed threshold, and a good agreement between both results. The stability of the NLMS algorithm in the presence of a small input signal is improved. The convergence speed of the C-NLMS ADF under noisy circumstances is also faster than that of the unconditioned ordinary NLMS ADF in the small tap number case. © 2001 Scripta Technica, Electr Eng Jpn, 136(4): 47–57, 2001 [ABSTRACT FROM AUTHOR]

It is important to get a steady-state operation of a power electronic circuit for its design. The shooting method, which is one of the steady-state analysis methods, solves a boundary value condition which equates initial values to final values after one-period transient. This paper proposes how to process the analysis in parallel by using a Parallel Virtual Machine (PVM3) system. In particular, the multiple shooting method (MSM) which divides the shooting time into subsections is suitable because it can parallel numerical processes for the divided shooting times by using multiple CPU units independently. This parallel method is applied to converter examples which are processes by PVM3. The computed results are investigated for their convergence and CPU times to check their parallel effects. According to the MSM algorithm, CPU times are reduced almost to one-fifth by using five computer units from a PVM3 system example. © 2001 Scripta Technica, Electr Eng Jpn, 135(2): 69–76, 2001 [ABSTRACT FROM AUTHOR]

Recently the authors proposed a simultaneous iteration algorithm for the computation of the partial derivatives of repeated eigenvalues and the corresponding eigenvectors of matrices depending on several real variables. This paper analyses the properties of that algorithm and extends it in several ways. The previous requirement that the repeated eigenvalue be dominant is relaxed, and the new generalized algorithm given here allows the simultaneous treatment of simple and repeated eigenvalues. Methods for accelerating convergence are examined. Numerical results support our theoretical analysis. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Lenstra-Lenstra-Lovász (LLL) is an effective lattice reduction algorithm for multiple-input multiple-output (MIMO) systems, which was considered to achieve full diversity in the MIMO fading channel. In the LLL algorithm, size reduction is performed for pairs of consecutive basis vectors, and the concern of numerical stability is raised. However, the whole complexity of the LLL algorithm is of polynomial order, and its characteristics of the convergence perform poor in MIMO system. In this paper, a variant version, named the novel hybrid algorithm, which combines both fix measurement and round measurement, is proposed. By modifying the iteration criterion and choosing proper values of the parameters, the algorithm has a large probability to skip the size reduction and cause a faster convergence, It means in one algorithm iteration the LLL potential can be reduced as much as possible. Also, the performance bound derived by the proximity factor shows that the hybrid LLL has a minor performance loss compared to the LLL algorithm. As a direct consequence, in simulation results, the hybrid LLL algorithm can make a better compromise between the rate of convergence, complexity of the algorithm, and algorithmic performance. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

The ChebFilterCG algorithm, proposed by Golub, Ruiz, and Touhami [SIAM J. Matrix Anal. Appl. 29 (2007), pp. 774-795] is an iterative method that combines Chebyshev filter and conjugate gradient for solving symmetric positive definite linear systems with multiple right-hand sides. The Chebyshev filter is used to produce initial residuals rich in eigenvectors corresponding to the smallest eigenvalues, which are then used in the initial phase of the conjugate gradient. This paper presents a convergence analysis of ChebFilterCG. In particular, it is shown theoretically and numerically that the algorithm yields an approximation of the invariant subspace associated with the smallest eigenvalues that can be recycled for solving several linear systems with the same matrix and different right-hand sides. A refined error bound when solving these systems is also given. The choice and influence of the Chebyshev filtering steps is discussed. Numerical experiments are described to illustrate that the Chebyshev filter does not degrade the distribution of the smallest eigenvalues and highlight the effect of rounding errors when large outlying eigenvalues are present. Finally, it is shown that the method may become more effective when an additional Chebyshev filtering step is used in the initialization phase of ChebFilterCG. [ABSTRACT FROM AUTHOR]

In this paper, we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, and C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix-Raviart nonconforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The geometric learning algorithm (GLA) was proposed as an application of the affine projection algorithm for an adaptive filter to the perceptron. In the GLA, the connection weight vector w(n) is updated vertically toward the orthogonal complement of k patterns. The GLA demonstrates some typical behavior when the learning rate λ is 2, which means that w(n) and w(n + 1) are symmetric with respect to the complement. Therefore, in this paper, the GLA with λ = 2 is discriminated as the symmetric learning algorithm (SLA) and the convergence properties of the SLA are analyzed. The convergence conditions regarding the order k of the SLA, the number P of patterns, and the dimension N of patterns are analyzed theoretically. It is proved that k < N is the necessary condition for convergence when P > 2N. The relation between k and the learning speed is analyzed theoretically. It becomes clear that the maximum learning speed on average can be obtained when k = N/2. These properties are supported by computer simulations. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 18–25, 1999 [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is proposed for finding a quasi-optimal schedule for the short-term thermal unit commitment problem taking LNG fuel constraints into account. In recent years, LNG fuel has been used increasingly. As a result, LNG fuel constraints should be considered in making a unit commitment schedule. Generally, unit commitment is a nonlinear combinatorial problem including discrete variables. To solve the problem, a two-step algorithm is developed using mathematical programming methods. First a linear programming problem is solved to determine the amount of LNG fuel to be consumed by each LNG unit, then a Lagrangian relaxation approach is used to obtain a unit commitment schedule. This two-step algorithm simplifies the problem and thus has good convergence characteristics. To test the effectiveness of the proposed algorithm, a numerical simulation was carried out on a 46-unit thermal system over a 24-hour period. A result with a dual gap of 0.00546 was obtained. © 1998 Scripta Technica, Electr Eng Jpn, 125(3): 22–30, 1998 [ABSTRACT FROM AUTHOR]

As an adaptive algorithm enabling pipelining, the delayed least mean square (DLMS) algorithm is well known. In a pipelined adaptive filter based on the conventional DLMS, the operating clock rate and the convergence characteristic are in a trade-off relationship, so that they cannot be improved at the same time. In this paper, a look-ahead-based DLMS (LDLMS) algorithm, as an extension of the DLMS based on the look-ahead transformation, and its pipelined processing configuration are proposed. By the proposed method, it is shown that the adaptive filter can carry out pipelined processing at a high operating clock rate without degrading the convergence characteristic. The proposed method is characterized by minimal possibility of the delay affecting the convergence property (effective delay) under a desired operating clock rate. Also, by means of computer simulation, the effectiveness of the proposed method is confirmed. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(1): 55–62, 1999 [ABSTRACT FROM AUTHOR]

This paper describes the predictive quantization of still pictures using the newly developed clustering with faster convergence than L.B.G. algorithm. In the proposed scheme, the input vector is separated into the average density and the deviation from the average (average density separated vector). Then the latter is quantized predictively using two code books of category 1 and category 2. Examining the utilization frequency of the codeword, the coding efficiency is improved by suppressing the redundancy. The code book of category 1 is designed using 256 codewords and successive clustering. Letting [i] be the codeword used in the quantization of the immediately preceding input vector, the code book of category 2 is composed of the set J([i]) with high probability to be used In the next quantization. It is predicted that the input data following the codeword [4] is quantized by an element of J([i]), and encoding is performed by the index attached to that element. The number of elements In J([i]) is 4 to 32 including the control code, which Is less than that of the coda book 1, realizing an improvement in the coding efficiency. If the codeword to be encoded is not found in J([i]), the code book 1 is used. The codewords in code book of category 1 are arranged in the order of their variances, which reduces the retrieval time in the code book co one-ninth to one-sixth the total retrieval clone. Using the proposed scheme and seven still pictures with 256 × 240 pixels and 256 gray scales as the training sequence, eleven pictures including the forementioned seven were encoded. The result revealed that 0.8 to 0.5 bits/pixel is required and the signal-to-noise ratio is 30 to 36 dB, indicating the excellent performance o£ the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper discusses convergence of the waveform relaxation method based on the decomposition of the circuit, and presents several sufficient conditions for the numerical procedure to converge locally. Then the block-diagonal dominant property is defined for the block matrix, and some properties of the block-diagonal dominant matrix are indicated. The algorithm in RELAX, which is a typical simulator based on the waveform relaxation method, is discussed. It is shown that the numerical procedure converges locally if the capacitance or conductance matrix is a block-diagonal dominant matrix. [ABSTRACT FROM AUTHOR]

Learning identification is one of the most widely utilized adaptive algorithms due to its small computational complexity. A problem with this algorithm is that a division by the square norm of the state vector is includ- ed in the coefficient update process which easily produces an instability when the nonstationary such as speech is given as the input. A method known to cope with such a problem and to realize the stable convergence involves not updating the coefficient when small input signals continue. This paper discusses this approach. As a first step, the situation is assumed where the square norm of the state vector is less than the specified threeshold and the effect of interrupting the coefficient update is analyzed. The convergence and the time-constant are formulated and the guarantee of the estimation accuracy for the convergence value is discussed. Then, the step gain is derived for the specified guarantee value so that the convergence speed is the fastest in the stochastic sense while ensuring stability. Lastly, the effectiveness of the proposed method is verified by computer simulation. It is shown that, even if the input signal is annotation, the fastest convergence speed is realized, together with the satisfactory estimation accuracy, which is always obtained according to the specified guarantee value after the convergence. [ABSTRACT FROM AUTHOR]

SPICE-type general-purpose circuit simulators are used widely as a support tool for circuit design. It often happens, however, that the dc operating-point analysis does not converge. To cope with such a situation, various approaches have been proposed based on continuation methods with the global convergence property, but these have yet to come to the stage of practical application to large-scale circuits. This paper proposes a practical algorithm which can be implemented on the general-purpose circuit simulators with modified nodal formulation, for determining the dc operating-point of large-scale circuits. As the first step, the concept of "modified cut-set analysis" is introduced and some properties of the modified nodal equation are presented. Then it is shown, in practical circuits, that the convergence of the algorithm is theoretically guaranteed. The proposed algorithm is then implemented on an existing general-purpose circuit simulator and applied to a bipolar analog LSI to demonstrate its effectiveness. For the LSI circuit formulated in 18,553 modified nodal equations, the dc operating point was determined in 270 minutes using an IBM RS6000-550. [ABSTRACT FROM AUTHOR]

Recently, extensive studies have been carried out on the algorithms which constructively determine the solution of nonlinear equations, These algorithms are in general attraction lies in the global convergence. However, fixed-point algorithms have been a problem in the execution speed is decreased greatly with the increase of the size of the system of equations to consider. This paper proposes a decomposition method and acceleration techniques as a means to improve the computational efficiency of the fixed point algorithms. Kevorkian's method is used in this paper as decomposition. Since the method includes errors in the decomposed equations and function value, it is important to discuss the convergence of the solution algorithm and to improve the convergence speed taking the effect of the those errors into consideration. This paper shows a solution algorithm in which the system of equations is decomposed by Kevorkian's method, and then Merril's method, a typical fixed-point algorithm, is applied. Accuracy of simplicial approximation and convergence properties of the algorithm are discussed, indicating that the algorithm exhibits local quadratic convergence under some suitable conditions. By numerical examples, it is verified that the algorithm exhibits quadratic convergence. The method is compared with the past methods, indicating the effectiveness of the propose method. [ABSTRACT FROM AUTHOR]

With the progress of hardware technology, the development of real-time adaptive algorithms is becoming more and more important. The essential questions concerning adaptive algorithms are: 1) increasing the speed of the algorithm; and 2) speeding up the convergence. It seems that the block signal processing and the orthogonal projection on the subspace of state-vectors are effective methods to solve the for mentioned questions 1) and 2), respectively. This paper proposes a block orthogonal projection algorithm (BOPA) which combines the block processing with the orthogonal projection operation. Next, an analysis of this algorithm is presented and the fundamental properties of the relation between the block length and the convergence characteristics arc shown. Also, the efficiency of the proposed algorithm is verified by computer simulation. This algorithm is based on a block- by-block adaptation where the operation of orthogonal projection on the state-vector space is performed repetitively for arbitrary blocks. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of weakly nonlinear complementarity problems arising from the discretization of free boundary problems. By reformulating the complementarity problems as implicit fixed-point equations based on splitting of the system matrices, we propose a class of modulus-based matrix splitting algorithms. We show their convergence by assuming that the system matrix is positive definite. Moreover, we give several kinds of typical practical choices of the modulus-based matrix splitting iteration methods based on the different splitting of the system matrix. Numerical experiments on two model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of our modulus-based matrix splitting algorithms. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a relaxed gradient based algorithm for solving extended Sylvester-conjugate matrix equations by considering a relaxation parameter is proposed. The convergence analysis of the algorithm is investigated. Theoretical analysis shows that the new method converges under certain assumptions.A numerical example is given to illustrate effectiveness of the proposed method and to test its efficiency compared with an existing one. [ABSTRACT FROM AUTHOR]

SUMMARY This paper customizes a contact detection and enforcing scheme to fit the three-dimensional (3-D) numerical manifold method (NMM). A hierarchical contact system is established for efficient contact detection. The mathematical mesh, a unique component in the NMM, is utilized for global searching of possible contact blocks and elements, followed by the local searching to identify primitive hierarchies. All the potential contact pairs are then transformed into one of the two essential entrance modes: point-to-plane and crossing-lines modes, among which real contact pairs are detected through a unified formula. The penalty method is selected to enforce the contact constraints, and a general contact solution procedure in the 3-D NMM is established. Because of the implicit framework, an open-close iteration is performed within each time step to determine the correct number of contact pairs among multi-bodies and to achieve complete convergence of imposed contact force at corresponding position. The proposed contact algorithm extensively utilizes most of the original components of the NMM, namely, the mathematical mesh/cells and the manifold elements, as well as the external components associated with contacts, such as the contact body, the contact facet and the contact vertex. In particular, the utilization of two mutually approaching mathematical cells is efficient in detecting contacting territory, which makes this method particularly effective for both convex and non-convex bodies. The validity and accuracy of the proposed contact algorithm are verified and demonstrated through three benchmark problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenvalue-eigenvector; (iii) the minimax theorem is satisfied without requiring the weak irreducibility condition; and (iv) if it is weakly reducible, then it can be decomposed into some weakly irreducible tensors. In addition, the problem of finding the largest eigenvalue of a symmetric nonnegative tensor is shown to be equivalent to finding the global solution of a convex optimization problem. Subsequently, algorithmic aspects for computing the largest eigenvalue of symmetric nonnegative tensors are discussed. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a second order [ABSTRACT FROM AUTHOR]