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A Unified Convergence Analysis for Some iterative algorithms with Applications to Fractional Calculus

International Journal of Applied and Computational Mathematics 2017年第2期3卷 323-332页

作者： Anastassiou, George A. Argyros, Ioannis K. Department of Mathematical Sciences University of Memphis Memphis 38152 TN United States Department of Mathematical Sciences Cameron University Lawton 73505 Ok United States

We present a local as well as a semilocal convergence analysis for some iterative algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the application part of the study, we present applications to fractional calculus by using some choices of the operators involving the left and right Caputo derivative, where the operators satisfy the convergence conditions. © 2016, Springer India Pvt. Ltd.

关键词： Banach space Fractional calculus Fractional derivatives iterative algorithm Semilocal-local convergence

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Scalability Evaluation of iterative algorithms Used for Supercomputer Simulation of Physical processes

Scalability Evaluation of Iterative Algorithms Used for Supe...

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Global Smart Industry Conference (GloSIC)

作者： Ezhova, Nadezhda A. Sokolinsky, Leonid B. South Ural State Univ Chelyabinsk Russia

ISBN: (纸本)9781538673867

The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on the BSF (Bulk Synchronous Farm) parallel computation model, which makes it possible to predict the upper scalability bound of an iterative algorithm in early phases of its design. The BSF model assumes the representation of the algorithm in the form of operations on lists using high-order functions. Two classes of representations are considered: BSF-M (Map BSF) and BSF-MR (Map-Reduce BSF). The proposed methodology is described by the example of the solution of the system of linear equations by the Jacobi method. For the Jacobi method, two iterative algorithms are constructed: Jacobi-M based on the BSF-M representation and Jacobi-MR based on the BSF-MR representation. Analytical estimations of the speedup, parallel efficiency and upper scalability bound are constructed for these algorithms using the BSF cost metrics on multiprocessor computing systems with distributed memory. An information about the implementation of these algorithms in C++ language using the BSF program skeleton and MPI parallel programming library are given. The results of large-scale computational experiments, performed on a cluster computing system, are demonstrated. Based on the experimental results, an analysis of the adequacy of estimations, obtained analytically by using the cost metrics of the BSF model, is made.

关键词： iterative algorithm parallel computation model BSF scalability estimation speedup parallel efficiency Jacobi method cluster computing systems

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iterative CHANNEL ESTIMATION AND DATA DETECTION algorithm FOR OTFS MODULATION 47

ITERATIVE CHANNEL ESTIMATION AND DATA DETECTION ALGORITHM FO...

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47th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Ouchikh, Rabah Aissa-El-Bey, Abdeldjalil Chonavel, Thierry Djeddou, Mustapha Ecole Mil Polytech Lab Telecommun Bordj El Bahri Algeria IMT Atlantique Lab STICC UMR CNRS 6285 F-29238 Brest France

ISBN: (纸本)9781665405409

In this paper, we design an iterative channel estimation and data detection algorithm in delay-Doppler domain for orthogonal time frequency space (OTFS) system by taking advantage of the sparse nature of the channel in this domain. The proposed algorithm iterates between message-passing-aided data detection and data-aided channel estimation. This sparse channel estimation is reformulated as a specific marginalization of maximum a posteriori (MAP) problem. To deal with the intractability of this problem, we provide a Bayesian approach based on the variational mean-field approximation via the variational Bayesian expectation maximization (VB-EM) algorithm. Finally, we compare the complexity and performance in term of Bit Error Rate (BER) and Normalized Mean Square Error (NMSE) of the proposed solution to a reference solution in the literature (SP-I).

关键词： OTFS channel estimation iterative algorithm Bayesian approach

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Generating Functional Analysis of iterative algorithms for Compressed Sensing

Generating Functional Analysis of Iterative Algorithms for C...

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IEEE International Symposium on Information Theory (ISIT)

作者： Mimura, Kazushi Hiroshima City Univ Dept Informat Sci Hiroshima 7313194 Japan

ISBN: (纸本)9781457705953

It has been shown that approximate message passing algorithm is effective in reconstruction problems for compressed sensing. To evaluate dynamics of such an algorithm, the state evolution (SE) has been proposed. If an algorithm can cancel the correlation between the present messages and their past values, SE can accurately tract its dynamics via a simple one-dimensional map. In this paper, we focus on dynamics of algorithms which cannot cancel the correlation and evaluate it by the generating functional analysis (GFA), which allows us to study the dynamics by an exact way in the large system limit.

关键词： algorithm design and analysis Approximation algorithms Compressed sensing Correlation GFA Heuristic algorithms iterative methods Random variables SE approximate message passing algorithm compressed sensing correlation theory functional analysis generating functional analysis iterative algorithm iterative methods one-dimensional map signal reconstruction state evolution

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Reviews of Recent Progress on Low-Complexity Linear Detection Via iterative algorithms for Massive MIMO Systems

Reviews of Recent Progress on Low-Complexity Linear Detectio...

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IEEE/CIC International Conference on Communication in China (ICCC)

作者： Zhang, Zhenyu Wu, Juan Ma, Xinli Dong, Yuanyuan Wang, Yingmin Chen, Shanzhi Dai, Xiaoming Univ Sci & Technol Beijing Inst Adv Network Technol & New Serv Beijing 100191 Peoples R China Univ Sci & Technol Beijing Beijing Engn & Technol Res Ctr Convergence Networ Beijing 100191 Peoples R China China Acad Telecommun Technol Beijing 100191 Peoples R China

ISBN: (纸本)9781509021369

Massive multiple-input multiple-output (MMIMO) can significantly enhance the spectrum efficiency of cellular networks by deploying hundreds of active elements at the base stations and is envisaged to become the key technology in 5th generation (5G) cellular networks. However, the large number of antennas required brings about tremendous challenges for practical implementation, especially for separation of the multiplexed data. iterative approaches, such as Jacobi, Richardson, Gauss-Seidel (GS), successive overrelaxation (SOR), and symmetric successive overrelaxation (SSOR) have received great attention recently due to their low-complexity and high performance for signal detection. In this work, we provide a comprehensive review of recent progress in iterative based signal detection for massive MIMO systems. The system model of an iterative method based minimum mean square error (MMSE) signal detection is provided. The convergence behavior and complexity of the iterative approach based detectors are analyzed. Numerical results show that the iterative algorithm-based detectors can achieve a performance close to the classical MMSE detector with significantly less computational complexity.

关键词： Massive multiple-input multiple-output (MIMO) minimum mean square error (MMSE) iterative algorithm convergence bit error rate (BER)

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Two Novel iterative algorithms for Interference Alignment with Symbol Extensions in the MIMO Interference Channel

Two Novel Iterative Algorithms for Interference Alignment wi...

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4th International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Wang, Chao Deng, Ke Li, Yubo Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Peoples R China

ISBN: (纸本)9781467358293;9781467358309

Interference alignment(IA) with symbol extensions in the K-user multiple-input multiple-output (MIMO) interference channel(IC) is considered in this paper. Symbol extensions produce the channels of special structure. Most of existing approaches are limited in cases where the channels have some special structure, because they align the interference without preserving the dimensionality of the desired signal. For that reason, two novel iterative algorithms for IA with symbol extensions are proposed. The first algorithm designs transceivers for IA based on minimizing the maximum per-user mean square error(MSE) while preserving the dimensionality of the desired signal. Utilizing channel reciprocity, the second algorithm is proposed which is the constrained optimization problem. It maximizes each receiver's SINR while preserving the dimensionality of the desired signal. The simulation results show that the proposed algorithms not only achieve good performance in terms of BER performance but also achieve good performance on maximizing sum rate of the system.

关键词： IA Interference alignment symbol extensions MIMO interference channel iterative algorithm mean square error

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iterative algorithms for solving the split feasibility problem in Hilbert spaces

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JOURNAL OF FIXED POINT THEORY AND APPLICATIONS 2018年第1期20卷 11-11页

作者： Zhao, Jing Zong, Haili Civil Aviat Univ China Tianjin Key Lab Adv Signal Proc Tianjin 300300 Peoples R China Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, we introduce two iterative algorithms for the split feasibility problem in real Hilbert spaces by reformulating it as a fixed point equation. Under suitable conditions, weak and strong convergence theorems are established. As a consequence, we obtain weak and strong convergence iterative sequences for the split equality problem introduced by Moudafi. The efficiency of the proposed algorithms is illustrated by numerical experiments. Our results improve and extend the corresponding results announced by many others.

关键词： Split feasibility problem iterative algorithm weak convergence strong convergence hilbert space

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iterative algorithms and convergence theorems for solving F-IGVIP and F-IGCP

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TAIWANESE JOURNAL OF MATHEMATICS 2007年第3期11卷 717-728页

作者： Lin, Yen-Cherng China Med Univ Gen Educ Ctr Taichung 404 Taiwan

In this paper, we study the iterative algorithm and convergence theorems for F-implicit generalized variational inequalities problem (F-IGVIP). By employing our earlier works ([6], Theorem 2.2), we establish several iterative convergence results for F-IGVIP. The algorithm and convergence results are new for solving the strong solution of F-IGVIP. Furthermore, new algorithms and convergence theorems for F-implicit generalized complementarity problem (F-IGCP) are also discussed.

关键词： iterative algorithm partially relaxed g-strongly monotone F-IGVIP F-IGCP

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An iterative Minimum Zone algorithm for assessing cylindricity deviation

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MEASUREMENT 2023年 213卷

作者： Liu, Fan Cao, Yanlong Li, Tukun Ren, Lifei Zhi, Junnan Yang, Jiangxin Jiang, Xiangqian Zhejiang Univ Coll Mech Engn Key Lab Adv Mfg Technol Zhejiang Prov Hangzhou 310027 Peoples R China Zhejiang Univ Coll Mech Engn State Key Lab Fluid Power & Mechatron Syst Hangzhou 310027 Peoples R China Univ Huddersfield Ctr Precis Technol Sch Comp & Engn EPSRC Future Adv Metrol Hub Huddersfield HD1 3DH England

This paper documents a novel fast method, named the iterative Minimum Zone algorithm (IMZA), for the evaluation of cylindricity deviation on a large number of measurement points, which plays a crucial role in the quality control of high-value products and components when a measurement is undertaken by a modern instrument, such as roundness tester, 3D laser/CT scanner. Firstly, the cylindricity deviation model and the minimum zone's theoretical basis are presented. Secondly, the Six-point-subset (SPS) and the replacement strategy are introduced, together with the detailed algorithm. The method strictly adheres to the latest ISO definition. A comparison between the proposed method and the typical approaches is carried out on both simulated data and measured data. The results show that IMZA can fast and accurately evaluate the cylindricity deviation with a large number of measurement points.

关键词： Cylindricity deviation Minimum zone iterative algorithm ISO GPS Tolerancing

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iterative inverse filter relaxation algorithm for adaptation to acoustic fluctuation in sound reproduction system

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2004年第7期87卷 15-26页

作者： Nagata, Y Tatekura, Y Saruwatari, H Shikano, K Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma 6300101 Japan

This paper proposes a relaxation algorithm for an inverse filter that is adaptive to environmental change in a multichannel sound reproduction system. For a conventional multichannel sound reproduction system, a design method has been proposed for an inverse filter by means of the Moore-Penrose-type generalized inverse matrix. However, in the inverse filter in the conventional method, background noise and line noise may be enhanced when the room transfer characteristics vary. In order to resolve this problem, an adaptive relaxation method based on the truncated singular value decomposition (TSVD) has been introduced. In the present paper, a microphone for monitoring the noise is placed at a location far from both ears of the listener. Relaxation of the inverse filter is carried out by using the reproduced sound observed by this microphone. From the results of computer simulation, it is found that the proposed method prevents amplification of the noise. Also, as a result of a subjective evaluation experiment on sound reproduction in a real acoustic environment, the sound quality was found to be improved significantly without damaging the sound localization of position. (C) 2004 Wiley Periodicals, Inc.

关键词： sound reproduction iterative algorithm inverse filter design adaptability relaxation of inverse filter

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