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Extended High Order algorithms for Equations under the Same Set of Conditions

algorithmS 2021年第7期14卷 207-207页

作者： Argyros, Ioannis K. Sharma, Debasis Argyros, Christopher I. Parhi, Sanjaya Kumar Sunanda, Shanta Kumari Argyros, Michael I. Cameron Univ Dept Math Sci Lawton OK 73505 USA IIIT Bhubaneswar Dept Math Bhubaneswar 751003 Odisha India Cameron Univ Dept Comp & Technol Lawton OK 73505 USA Fakir Mohan Univ Dept Math Balasore 756020 Odisha India Univ Oklahoma Dept Comp Sci Norman OK 73071 USA

A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order. More importantly, bounds on error and uniqueness regions for the solution are also not derived. Therefore, the benefits of these algorithms are limited. We simply use the first derivative to tackle all these issues and study the ball analysis for two sixth order algorithms under the same set of conditions. In addition, we present a calculable ball comparison between these algorithms. In this manner, we enhance the utility of these algorithms. Our idea is very general. That is why it can also be used to extend other algorithms as well in the same way.

关键词： Banach spaces iterative algorithm Frechet derivative attraction basin local convergence convergence ball

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Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

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HELIYON 2021年第7期7卷 e07499页

作者： Yahaya, Mahmoud Muhammad Kumam, Poom Awwal, Aliyu Muhammed Aji, Sani King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math Ctr Excellence Theoret & Computat Sci TaCS CoE 126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math KMUTTFixed Point Res Lab 126 Pracha Uthit RdRoom SCL 802 Fixed Point Lab Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE BNCAO Res CtrFixed Point Theory & Applicat Res G 126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi Fac Sci Dept Math 126 Pracha Uthit Rd Bangkok 10140 Thailand Gombe State Univ Fac Sci Dept Math Gombe 760214 Nigeria

The study of efficient iterative algorithms for addressing nonlinear least-squares (NLS) problems is of great importance. The NLS problems, which belong to a special class of unconstrained optimization problems, are of particular interest because of the special structure of their gradients and Hessians. In this paper, based on the spectral parameters of Barzillai and Borwein (1998), we propose three structured spectral gradient algorithms for solving NLS problems. Each spectral parameter in the respective algorithms incorporates the structured gradient and the information gained from the structured Hessian approximation. Moreover, we develop a safeguarding technique for the first two structured spectral parameters to avoid negative curvature directions. Moreso, using a nonmonotone line-search strategy, we show that the proposed algorithms are globally convergent under some standard conditions. The comparative computational results on some standard test problems show that the proposed algorithms are efficient.

关键词： iterative algorithm Spectral gradient algorithm Nonlinear least squares Line-search Quasi-Newton algorithm

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MuSP: A multistep screening procedure for sparse recovery

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STAT 2021年第1期10卷

作者： Yang, Yuehan Zhu, Ji George, Edward, I Cent Univ Finance & Econ Dept Stat Beijing 100081 Peoples R China Univ Michigan Dept Stat Ann Arbor MI 48109 USA Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA

We propose a multistep screening procedure (MuSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations. Specifically, in each iteration, an adaptive lasso regression with a small penalty is fit within the reduced feature space obtained from the previous step, rendering its computational complexity roughly comparable with the Lasso. MuSP is shown to select the true model under complex correlation structures among the predictors and response, even when the irrepresentable condition fails. Further, under suitable regularity conditions, MuSP achieves the optimalminimax rate (q log n/n)(1/2) for the upperbound of l(2)-norm error. Numerical comparisons show that the method works effectively both in model selection and estimation, and the MuSP fitted model is stable over a range of small tuning parameter values, eliminating the need to choose the tuning parameter by cross-validation. We also apply MuSP to financial data and show that MuSP is successful in asset allocation selection.

关键词： high-dimensional data iterative algorithm Lasso multistep method

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Estimation method of cable tension based on iterative algorithm and optimization algorithm

Estimation method of cable tension based on iterative algori...

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3rd International Conference on Civil Engineering, Architecture and Building Materials (CEABM 2013)

作者： Huang, Yong-hui Luo, De-quan Rao, Rui Guangzhou Univ Guangzhou Univ Tamkang Univ Joint Res Ctr Engn St Guangzhou 510006 Guangdong Peoples R China South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510640 Peoples R China

ISBN: (纸本)9783037857755

The vibration method is usually used for field measurement of cable tension of cable system bridges. The cable tension evaluation method is mostly based on the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications especially for the cables with big bending stiffness and two ends fixed boundary conditions. In this paper a cable tension estimation method based on iterative algorithm and optimization algorithm is presented and implemented using finite element method and ANSYS soft ware. Compared with the analytical method and empirical formulas the method presented in this paper is more convenient and the application range is more extensive. The accuracy of the method has been verified by a set of test. In the end, the method is used to estimate the cable tension of a tied-arch bridge's suspenders.

关键词： Cable tension estimation frequency method iterative algorithm optimization algorithm

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iterative criteria for identifying strong H-tensors

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 352卷 93-109页

作者： Huang, Baohua Ma, Changfeng Fujian Normal Univ Coll Math & Informat Fuzhou 350117 Fujian Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Fujian Peoples R China

Strong H-tensors play an important role in the theories and applications of numerical linear algebra. It is necessary to identify whether a given tensor is a strong H-tensor or not. In this paper, we establish some iterative criteria for identifying strong H-tensors. These criteria depend on the elements of the tensors: therefore, they are easy to be verified. The results obtained in this paper extend the corresponding conclusions for strictly generalized diagonally dominant matrices. As an application, some sufficient conditions for the positive definiteness of an even-order real symmetric tensor are presented. Some numerical experiments show the feasibility and efficiency of the results which are obtained in this paper. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Strong H-tensors Strictly generalized diagonally dominant iterative algorithm Positive definiteness Numerical experiments

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An iterative algorithm for Differentially Private Histogram Publication

An Iterative Algorithm for Differentially Private Histogram ...

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International Conference on Cloud Computing and Big Data (CLOUDCOM-ASIA)

作者： Chen, Hong Wu, Yingjie Chen, Tingting Wang, Xiaodong Fuzhou Univ Coll Math & Comp Sci Fuzhou 350108 Peoples R China

ISBN: (纸本)9781479928293

Traditionally, the accuracy of range queries in differentially private histogram publication was boosted by obtaining the Best Linear Unbiased Estimator (BLUE) of the nodes' noisy values in the Differential Privacy Range Tree (DPRT). However, exist works require DPRT be perfect k-ary, which means it is not suitable for differentially private histogram publication under arbitrary tree structure In this paper, we propose an efficient iterative algorithm GBLUE for differential privacy histogram publication based on any tree structure. The correctness of GBLUE is guaranteed by theoretical analysis and experimental demonstration. Experimental results show that GBLUE is effective and feasible.

关键词： differential privacy iterative algorithm histogram publication

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A Current-Driven Six-Channel Potentiostat for Rapid Performance Characterization of Microbial Electrolysis Cells

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2019年第12期68卷 4694-4702页

作者： Molderez, Tom R. Zhang, Xu Rabaey, Korneel Verhelst, Marian Katholieke Univ Leuven Dept Elect Engn ESAT MICAS B-3000 Leuven Belgium Univ Ghent Ctr Microbial Ecol & Technol B-9000 Ghent Belgium

Knowledge of the performance of microbial electrolysis cells under a wide range of operating conditions is crucial to achieve high production efficiencies. Characterizing this performance in an experiment, however, is challenging due to either the long measurement times of steady-state procedures or the transient errors of dynamic procedures. Moreover, wide parallelization of the measurements is not feasible due to the high measurement equipment cost per channel. Hence, to speedup this characterization and to facilitate low-cost, yet widely parallel measurements, this paper presents a novel rapid polarization curve measurement procedure with a dynamic measurement resolution that runs on a custom six-channel potentiostat with a current-driven topology. As case study, the procedure is used to rapidly assess the impact of altering pH values on a microbial electrolysis cell that produces H-2. A $\times 2$ - $\times 12$ speedup could be obtained in comparison with the state-of-the-art, depending on the characterization resolution (16-128 levels). On top of this speedup, measurements can be parallelized up to $6\times $ on the presented, affordable-42-per-channel-potentiostat.

关键词： Analog circuits bioelectric phenomena closed-loop systems electrochemical devices iterative algorithm measurement microorganisms PI-control real-time systems search methods

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Image compressive recovery based on dictionary learning from under-sampled measurement

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MULTIMEDIA TOOLS AND APPLICATIONS 2019年第5期78卷 5169-5180页

作者： Zhao, Feng Si, Weijian Dou, Zheng Wu, Qidi Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Heilongjiang Peoples R China

Compressive sensing(CS) has attracted many attentions in recent years, which assumes that the signal can be exactly reconstruction from its only a few measurements when it is sparsity enough under a certain domain. In this paper, we address the image compressive recovery problem. Firstly, a specific adaptive dictionary learning method is adopted to represent the image more sparsely, which learns atoms in dictionary from the under-sampled measurement directly and shows some good performance in adapting to the compressed sensing framework. Secondly, by utilizing the nonlocal self-similarity in image, we also propose a novel nonlocal CS model with multiple regularizations to preserve the details in the reconstruction image, which are seen as the important information to human perception. In addition, to further improve the computational efficiency, an iterative algorithm is developed to solve the proposed model effectively. Extensive experiments on various benchmark images verify that, compared to the existing excellent methods, the proposed model shows superior and competitive performance.

关键词： Compressed sensing Image recovery Dictionary learning Nonlocal technique iterative algorithm

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iterative solution of Helmert transformation based on a unit dual quaternion

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ACTA GEODAETICA ET GEOPHYSICA 2019年第1期54卷 123-141页

作者： Zeng, Huaien Chang, Guobin He, Haiqing Tu, Yi Sun, Shuifa Wu, Yue China Three Gorges Univ Natl Field Observat & Res Stn Landslides Three Go Yichang 443002 Peoples R China China Three Gorges Univ Hubei Key Lab Intelligent Vis Based Monitoring Hy Yichang 443002 Peoples R China China Three Gorges Univ Hubei Key Lab Construct & Management Hydropower E Yichang 443002 Peoples R China China Univ Min & Technol Sch Environm Sci & Spatial Informat Xuzhou 221116 Jiangsu Peoples R China East China Univ Technol Sch Geomat Nanchang 330013 Jiangxi Peoples R China China Three Gorges Univ Key Lab Geol Hazards Three Gorges Reservoir Area Minist Educ Yichang 443002 Peoples R China

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66-76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al.

关键词： Helmert transformation Dual quaternion iterative algorithm Initial value of parameter Geodetic coordinate transformation

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A Novel Dehazing Method for Color Fidelity and Contrast Enhancement on Mobile Devices

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2019年第1期65卷 47-56页

作者： Wang, Ping Fan, Qinglan Zhang, Yunfeng Bao, Fangxun Zhang, Caiming Shandong Univ Finance & Econ Dept Comp Sci & Technol Jinan 250014 Shandong Peoples R China Shandong Univ Dept Math Jinan 250100 Shandong Peoples R China Shandong Univ Dept Comp Sci & Technol Jinan 250100 Shandong Peoples R China

Mobile devices that can capture images outdoors often suffer from poor weather conditions. Observed scenes lose contrast and visibility, and are also subject to color shifts due to the presence of fog and haze. In this paper, a single image dehazing method for removing color distortion and enhancing contrast on mobile devices is presented. The method can effectively remove haze from images with an uneven haze density. First, based on the local haze density, a superpixel segmentation algorithm is employed to adaptively divide a hazy image into several regions. Second, the local atmospheric light in each image region is estimated, and an initial transmission map is calculated. Finally, based on the haze imaging model, an iterative algorithm is developed to estimate the local atmospheric light and transmission for restoring the image. The proposed method can effectively recover detailed image information, resulting in an image with natural color, with an acceptable time performance. Experimental results show that the proposed method can be applied effectively to mobile devices, including digital cameras and mobile phones for enhancing the contrast and visibility without introducing color distortion.

关键词： Single image dehazing region division local atmospheric light iterative algorithm

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