• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.715-723
• /
• 2009

The aim of this paper is to present an explicit iteration method for finding a common fixed point of a finite family of strictly pseudocon-tractive mappings defined on q-uniformly smooth and uniformly convex Banach spaces.

• Journal of applied mathematics & informatics
• /
• v.39 no.3_4
• /
• pp.587-600
• /
• 2021

Some problems in engineering and science can be equivalently transformed into solving multi-linear systems. In this paper, we propose two preconditioned AOR iteration methods to solve multi-linear systems with -tensor. Based on these methods, the general conditions of preconditioners are given. We give the convergence theorem and comparison theorem of the two methods. The results of numerical examples show that methods we propose are more effective.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.785-795
• /
• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• Journal of information and communication convergence engineering
• /
• v.8 no.2
• /
• pp.228-233
• /
• 2010

In this paper, the iteration localization algorithm that NLOS signal is iteratively removed to get the exact location in the wireless sensor network is proposed. To evaluate the performance of the proposed algorithm, TDOA location estimation method is used, and readers are located on every 150m intervals with rectangular shape in $300m{\times}300m$ searching field. In that searching field, the error distance is analyzed according to increasing the number of iteration, sub-blink and the estimated sensor node locations which are located in the iteration range. From simulation results, the error distance is diminished according to increasing the number of the sub-blink and iteration with the proposed location estimation algorithm in NLOS environment. Therefore, to get more accurate location information in wireless sensor network in NLOS environments, the proposed location estimation algorithm removing NLOS signal effects through iteration scheme is suitable.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.7
• /
• pp.3338-3355
• /
• 2018

Images acquired by Large Aperture Static Imaging Spectrometer (LASIS) exhibit obvious interference stripes, which are vertical and stationary due to the special imaging principle of interference hyperspectral image (IHI) data. As the special characteristics above will seriously affect the intrinsic structure and sparsity of IHI, decomposition of IHI has drawn considerable attentions of many scientists and lots of efforts have been made. Although some decomposition methods for interference hyperspectral data have been proposed to solve the above problem of interference stripes, too many times of iteration are necessary to get an optimal solution, which will severely affect the efficiency of application. A novel algorithm for decomposition of interference hyperspectral images based on split Bregman iteration is proposed in this paper, compared with other decomposition methods, numerical experiments have proved that the proposed method will be much more efficient and can reduce the times of iteration significantly.

• Interaction and multiscale mechanics
• /
• v.1 no.2
• /
• pp.211-230
• /
• 2008

Owing to the growing size of the eigenvalue problem and the growing number of eigenvalues desired, solution methods of iterative nature are becoming more popular than ever, which however suffer from low efficiency and lack of proper convergence criteria. In this paper, three efficient iterative eigenvalue algorithms are considered, i.e., subspace iteration method, iterative Ritz vector method and iterative Lanczos method based on the cell sparse fast solver and loop-unrolling. They are examined under the mode error criterion, i.e., the ratio of the out-of-balance nodal forces and the maximum elastic nodal point forces. Averagely speaking, the iterative Ritz vector method is the most efficient one among the three. Based on the mode error convergence criteria, the eigenvalue solvers are shown to be more stable than those based on eigenvalues only. Compared with ANSYS's subspace iteration and block Lanczos approaches, the subspace iteration presented here appears to be more efficient, while the Lanczos approach has roughly equal efficiency. The methods proposed are robust and efficient. Large size tests show that the improvement in terms of CPU time and storage is tremendous. Also reported is an aggressive shifting technique for the subspace iteration method, based on the mode error convergence criteria. A backward technique is introduced when the shift is not located in the right region. The efficiency of such a technique was demonstrated in the numerical tests.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.16 no.4
• /
• pp.1330-1350
• /
• 2022

As a preprocessing operation of transmitter antennas, the hybrid precoding is restricted by the limited computing resources of the transmitter. Therefore, this paper proposes a novel hybrid precoding that guarantees the communication efficiency with low complexity and a fast computational speed. First, the analog and digital precoding matrix is derived from the maximum eigenvectors of the channel matrix in the sub-connected architecture to maximize the communication rate. Second, the extended power iteration (EPI) is utilized to obtain the maximum eigenvalues and their eigenvectors of the channel matrix, which reduces the computational complexity caused by the singular value decomposition (SVD). Third, the Aitken acceleration method is utilized to further improve the convergence rate of the EPI algorithm. Finally, the hybrid precoding based on the EPI method and the Aitken acceleration algorithm is evaluated in millimeter-wave (mmWave) massive multiple-input and multiple-output (MIMO) systems. The experimental results show that the proposed method can reduce the computational complexity with the high performance in mmWave massive MIMO systems. The method has the wide application prospect in future wireless communication systems.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.8A
• /
• pp.1254-1264
• /
• 2000

In this paper, we propose a new turbo interleaver and an efficient iteration control method with low complexity for turbo decoding. Turbo codes has better performance as the number of iteration and the interleaver size increases. However, as the interleaver size is increased, it require much delay and computation for decoding. Thus we propose a new efficient turbo magic interleaver using the Magic square matrix. Simulation results show that the proposed interleaver realizes a good performance like GF, Mother interleaver proposed to IMT-2000. And as the decoding approaches the performance limit, any further iteration results in very little improvement. Therefore, we propose an efficient algorithm of decoding that can reduce the delay and computation. Just like the conventional stop criterion, it effectively stop the iteration process with very little performance degradation.

• Journal of Mechanical Science and Technology
• /
• v.20 no.11
• /
• pp.1950-1960
• /
• 2006

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.7 no.9
• /
• pp.2284-2298
• /
• 2013

In this paper, a fast and efficient signal reconstruction algorithm for solving the basis pursuit (BP) problem in compressed sensing (CS) is proposed. This fast linearized Bregman method (FLBM), which is inspired by the fast method of Beck et al., is based on the fact that the linearized Bregman method (LBM) is equivalent to a gradient descent method when applied to a certain formulation. The LBM requires $O(1/{\varepsilon})$ iterations to obtain an ${\varepsilon}$-optimal solution while the FLBM reduces this iteration complexity to $O(1/\sqrt{\varepsilon})$ and requiring almost the same computational effort on each iteration. Our experimental results show that the FLBM can be faster than some other existing signal reconstruction methods.