• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.961-969
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• 2021

In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.1-25
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• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.1-11
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• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.59-82
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• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.4
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• pp.462-469
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• 2002

While the conventional K-means algorithms use a fixed weight to design a vector codebook for all learning iterations, the proposed method employs a variable weight for learning iterations. The weight value of two or more beyond a convergent region is applied to obtain new codevectors at the initial learning iteration. The number of learning iteration applying a variable weight must be decreased for higher weight value at the initial learning iteration to design a better codebook. To enhance the splitting method that is used to generate an initial codebook, we propose a new method, which reduces the error between a representative vector and the member of training vectors. The method is that the representative vector with maximum squared error is rejected, but the vector with minimum error is splitting, and then we can obtain the better initial codevectors.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.5
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• pp.1649-1665
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• 2021

In view of the low accuracy of the traditional FunkSVD algorithm, and in order to improve the computational efficiency of the algorithm, this paper proposes a parallel algorithm of improved FunkSVD based on Spark (SP-FD). Using RMSProp algorithm to improve the traditional FunkSVD algorithm. The improved FunkSVD algorithm can not only solve the problem of decreased accuracy caused by iterative oscillations but also alleviate the impact of data sparseness on the accuracy of the algorithm, thereby achieving the effect of improving the accuracy of the algorithm. And using the Spark big data computing framework to realize the parallelization of the improved algorithm, to use RDD for iterative calculation, and to store calculation data in the iterative process in distributed memory to speed up the iteration. The Cartesian product operation in the improved FunkSVD algorithm is divided into blocks to realize parallel calculation, thereby improving the calculation speed of the algorithm. Experiments on three standard data sets in terms of accuracy, execution time, and speedup show that the SP-FD algorithm not only improves the recommendation accuracy, shortens the calculation interval compared to the traditional FunkSVD and several other algorithms but also shows good parallel performance in a cluster environment with multiple nodes. The analysis of experimental results shows that the SP-FD algorithm improves the accuracy and parallel computing capability of the algorithm, which is better than the traditional FunkSVD algorithm.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.3
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• pp.73-81
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• 2004

To extract the creditable features in fingerprint image, many people use the thinning algorithm that has a very important position in the preprocessing. In this paper, we propose the robust parallel thinning algorithm that can preserve the connectivity of the binarized fingerprint image, make the thinnest skeleton with 1-pixel width and get near to the medial axis extremely. The proposed thinning method repeats three sub-iterations. The first sub-iteration takes off only the outer boundary pixel by using the interior points. To extract the one side skeletons, the second sub-iteration finds the skeletons with 2-pixel width. The third sub-iteration prunes the needless pixels with 2-pixel width existing in the obtained skeletons and then the proposed thinning algorithm has the robustness against the rotation and noise and can make the balanced medial axis. To evaluate the performance of the proposed thinning algorithm we compare with and analyze the previous algorithms.

• Animal cells and systems
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• v.4 no.1
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• pp.31-37
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• 2000

The genetic variations among six species of Rana from Korea (R. nigro-maculata, R. piancyi, R. dybowskii, R. sp, R. rugosa type A, B and R. amurensis) were investigated using 499 bases of mitochondrial DNA sequences for ND2 (NADH dehydrogenase subunit 2) gene and $tRNA^{Trp}$ gene. Partial sequences of ND2 gene (427 bp) and full sequences of $tRNA^{Trp}$ gene (73 bp) were identified. The level of sequence divergences ranged from 0.2 to 5.2% within species and 4.9-28.0% among 6 species of the genus Rana. The $tRNA^{Trp}$ gene of the genus Rana was composed of 77 nucleotides which showed a two dimensional "cloverleaf" structure. The secondary structure of $tRNA^{Trp}$ was not found compensatory changes which could potentially confound phylogenetic inference. In the neighborjoining tree, brown frogs were clustered first with the level of sequence divergence of 13.20% between R. amurensis and R. dybowskii, and 9% between R. dybowskii and R. sp. supported by 99% bootstrap iterations, respectively. R. nigromaculata and R. plancyi were clustered into another group with 5.1% divergence supported by 100% bootstrap iteration. R. rugosa A 8nd B types were grouped by 4.9% divergence and clustered into the last group with other two groups with 100% bootstrap iterations.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.9
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• pp.2087-2093
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• 2014

In this paper, an orthogonal matching pursuit (OMP) method combined with genetic algorithm (GA), named GAOMP, is proposed for sparse signal recovery. Some recent greedy algorithms such as SP, CoSaMP, and gOMP improved the reconstruction performance by deleting unsuitable atoms at each iteration. However they still often fail to converge to the solution because the support set could not avoid the local minimum during the iterations. Mutating the candidate support set chosen by the OMP algorithm, GAOMP is able to escape from the local minimum and hence recovers the sparse signal. Experimental results show that GAOMP outperforms several OMP based algorithms and the $l_1$ optimization method in terms of exact reconstruction probability.