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This paper aims to present a dynamically adjusted deflated restarting procedure for the generalized conjugate residual method with an inner orthogonalization (GCRO) method.

The proposed method uses a GCR solver for the outer iteration and the generalized minimal residual (GMRES) with deflated restarting in the inner iteration. Approximate eigenpairs are evaluated at the end of each inner GMRES restart cycle. The approach determines the number of vectors to be deflated from the spectrum based on the number of negative Ritz values, k∗.

The authors show that the approach restores convergence to cases where GMRES with restart failed and compare the approach against standard GMRES with restarts and deflated restarting. Efficiency is demonstrated for a 2D NACA 0012 airfoil and a 3D common research model wing. In addition, numerical experiments confirm the scalability of the solver.

This paper proposes an extension of dynamic deflated restarting into the traditional GCRO method to improve convergence performance with a significant reduction in the memory usage. The novel deflation strategy involves selecting the number of deflated vectors per restart cycle based on the number of negative harmonic Ritz eigenpairs and defaulting to standard restarted GMRES within the inner loop if none, and restricts the deflated vectors to the smallest eigenvalues present in the modified Hessenberg matrix.

The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).

Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method.

This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed.

The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field.

The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation.

Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated.

It can be seen that the nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. The verification of proposed method is demonstrated using practical nonlinear magnetic field problem.

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures.

The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition.

It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results.

An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

Achieving natural interactions by means of vision and speech between humans and robots is one of the major goals that many researchers are working on. This paper aims to describe a gesture‐based human‐robot interaction (HRI) system using a knowledge‐based software platform.

A frame‐based knowledge model is defined for the gesture interpretation and HRI. In this knowledge model, necessary frames are defined for the known users, robots, poses, gestures and robot behaviors. First, the system identifies the user using the eigenface method. Then, face and hand poses are segmented from the camera frame buffer using the person's specific skin color information and classified by the subspace method.

The system is capable of recognizing static gestures comprised of the face and hand poses, and dynamic gestures of face in motion. The system combines computer vision and knowledge‐based approaches in order to improve the adaptability to different people.

Provides information on an experimental HRI system that has been implemented in the frame‐based software platform for agent and knowledge management using the AIBO entertainment robot, and this has been demonstrated to be useful and efficient within a limited situation.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.

In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.

This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.

The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

The purpose of this paper is to introduce efficient methods for solving the 2D biharmonic equation with Dirichlet boundary conditions of second kind. This equation describes the deflection of loaded plate with boundary conditions of simply supported plate kind. Also it can be derived from the calculus of variations combined with the variational principle of minimum potential energy. Because of existing fourth derivatives in this equation, introducing high‐order accurate methods need to use artificial points. Also solving the resulted linear system of equations suffers from slow convergence when iterative methods are used. This paper aims to introduce efficient methods to overcome these problems.

The paper considers several compact finite difference approximations that are derived on a nine‐point compact stencil using the values of the solution and its second derivatives as the unknowns. In these approximations there is no need to define special formulas near the boundaries and boundary conditions can be incorporated with these techniques. Several iterative linear systems solvers such as Krylov subspace and multigrid methods and their combination (with suitable preconditioner) have been developed to compare the efficiency of each method and to design powerful solvers.

The paper finds that the combination of compact finite difference schemes with multigrid method and Krylov iteration methods preconditioned by multigrid have excellent results for the second biharmonic equation, and that Krylov iteration methods preconditioned by multigrid are the most efficient methods.

The paper is of value in presenting, via some tables and figures, some numerical experiments which resulted from applying new methods on several test problems, and making comparison with conventional methods.

The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.

By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated.

The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.

Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency.

For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.

Direction-of-arrival (DOA) estimation for wideband sources has attracted a growing interest in the recent decade because wideband sources are incorporated in many real-world applications such as communication systems, radar, sonar and acoustics. One way to estimate the DOAs of wideband signals is to decompose it into narrowband signals using discrete Fourier transform (DFT) and then apply well-established narrowband algorithms to each signal. Afterwards, results are averaged to yield the final DOAs. These techniques require scanning the full band of wideband sources, ultimately degrading the resolution and increasing complexity. This paper aims to propose a new DOA estimation methodology to solve these problems.

The new DOA estimation methodology is based on incoherent signal subspace method (ISSM). The proposed approach presents a criterion to select a single sub-band of the selected narrowband signals instead of scanning the whole signal spectrum. Then, the DOAs of wideband signals are estimated using the selected sub-band. Therefore, it is named as single sub-band (SSB)-ISSM.

The computational complexity of the proposed method is much lower than that of traditional DFT-based methods. The effectiveness and advantages of the proposed methodology are theoretically investigated, and computational complexity is also addressed.

To verify the theoretical analysis, computer simulations are implemented, and comparisons with other algorithms are made. The simulation results show that the proposed method achieves better performance and accurately estimates the DOAs of wideband sources.

Transaction cost becomes significant when one holds many securities in a large portfolio where capital allocations are frequently rebalanced due to variations in non-stationary statistical characteristics of the asset returns. The purpose of this paper is to employ a sparsing method to sparse the eigenportfolios, so that the transaction cost can be reduced and without any loss of its performance.

In this paper, the authors have designed pdf-optimized mid-tread Lloyd-Max quantizers based on the distribution of each eigenportfolio, and then employed them to sparse the eigenportfolios, so those small size orders may usually be ignored (sparsed), as the result, the trading costs have been reduced.

The authors find that the sparsing technique addressed in this paper is methodic, easy to implement for large size portfolios and it offers significant reduction in transaction cost without any loss of performance.

In this paper, the authors investigated the performance the sparsed eigenportfolios of stock returns in S&P500 Index. It is shown that the sparsing method is simple to implement and it provides high levels of sparsity without causing PNL loss. Therefore, transaction cost of managing a large size portfolio is reduced by employing such an efficient sparsity method.

Classical techniques to estimate the spectrum of the multi‐component signal are based on Fourier‐based transformations. The frequency estimates obtained from their spectral peaks are affected by the window length and phase of signal component, thus presenting a large variance even in the absence of noise. The spectrum of the signals is estimated with the help of the Wigner‐Ville distribution and its time‐frequency representation is obtained. For the same purpose, the min‐norm method (subspace method) is used. The accuracy of the tested methods was investigated and compared with the parameters of the frequency estimation via FFT. The proposed methods were also tested with non‐stationary multiple‐component signals occurring during the fault operation of inverter‐fed drives and transmission lines.