The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establis...
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The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green's function approach and its implications for various scientific and engineering applications, paving the way for future research in this area.
Usurelu et al. (Int J Comput Math 98:1049-1068, 2021) presented stability and data dependence results for a TTP (Thakur-Thakur-Postolache) iteration algorithm associated with quasi-strictly contractive mappings and co...
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Usurelu et al. (Int J Comput Math 98:1049-1068, 2021) presented stability and data dependence results for a TTP (Thakur-Thakur-Postolache) iteration algorithm associated with quasi-strictly contractive mappings and contraction mappings, respectively, but these results were subject to strong conditions on the parametric control sequences used in the TTP iteration algorithm. This article aims to expand those results conducting a thorough analysis of the convergence of TTP and S iteration algorithms and improve those results by removing the restrictions on the parametric control sequences. Additionally, a data dependence result for the TTP iteration algorithm of quasi-strictly contractive mappings is established and several collage theorems are introduced to offer new insights into the data dependence of fixed points of quasi-strictly contractive mappings and to solve related inverse problems. In order to exhibit the dependability and effectiveness of all the results discussed in this work, a multitude of numerical examples are furnished, encompassing both linear and nonlinear differential equations (DEs) and partial differential equations (PDEs). This work can be viewed as an important refinement and complement to the study by Usurelu et al. (Int J Comput Math 98:1049-1068, 2021).
Multi-metric learning is important for improving classification performance since learning a single metric is usually insufficient for complex data. The existing multi-metric learning methods are based on the triplet ...
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Multi-metric learning is important for improving classification performance since learning a single metric is usually insufficient for complex data. The existing multi-metric learning methods are based on the triplet constraints, and thus are with high computing complexity. In this work, we propose an efficient multi-metric learning framework by a pair of two-metric learning schemes (called TMML) to jointly train two local metrics and a global metric, where the distances between samples are automatically adjusted to maximize classification margin. Instead of the triplet constraints, the proposed TMML is based on the pair constraints to reduce the computational burden. Moreover, a global regularization is introduced to improve generalization and control overfitting. The proposed TMML improves the limitation of a single metric, where a pair of local metrics are interrelated to conduct adaptation for the local characteristics, while global metrics are to depict the common properties from all the data. Furthermore, we develop an alternating direction iterative algorithm to optimize the proposed TMML. The convergence of the algorithm is analyzed theoretically. Numerical experiments are carried out on different scale datasets. Under different evaluation criteria, experiments show that the proposed TMML is superior to the single metric learning methods, and achieves better performance than other state-of-the-art multi-metric learning methods in most cases.
As the output characteristic of photovoltaic arrays is a non-linear function of external environment, the step-size of maximum power point tracking (MPPT) algorithm should be regulated dynamically to improve the MPPT ...
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As the output characteristic of photovoltaic arrays is a non-linear function of external environment, the step-size of maximum power point tracking (MPPT) algorithm should be regulated dynamically to improve the MPPT efficiency. However, the step-size, essentially determining the performance of MPPT algorithm, is often designed for a particular system with certain working conditions. To solve this problem, an optimisation algorithm is proposed in this study, which can adjust the step-size automatically. From the essence of optimisation problem, the tracking process can be converted into a maximum sequence which can be solved by several iteration algorithms. This study provides a simple and effective way to obtain the step-size. Once the iteration method is selected, the performance of the MPPT algorithm has been decided. The analysis of convergence, convergence order and stability are presented in this study. Comprehensive simulation and experimental results demonstrate that this proposed algorithm has a good stable and dynamic characteristic.
The paper considers the numerical solution of boundary-value problems for multidimensional convection-diffusion type equations (CDEs). Such equations are useful for various physical processes in solids, liquids and ga...
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The aim of this paper is to study a finite family of H-accretive operators and prove common zero point theorems of them in Banach space. The results presented in this paper extend and improve the corresponding results...
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The aim of this paper is to study a finite family of H-accretive operators and prove common zero point theorems of them in Banach space. The results presented in this paper extend and improve the corresponding results of Zegeye and Shahzad (Nonlinear Anal 66: 1161-1169, 2007), Liu and He (J Math Anal Appl 385: 466-476, 2012) and the related results.
The core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribu...
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The core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribution by straightforward Fourier synthesis is usually hindered due to the well known phase problem and the finite resolution of diffraction data. In analogy with optical imaging systems, the reconstructed electron-density map may be regarded as the image of the real electron-density distribution in crystals. Inspired by image definition evaluation functions applied in the auto-focusing process, two evaluation functions are proposed for the reconstructed electron-density images. One of them is based on the atomicity of the electron-density distribution and properties of Fourier synthesis. Tests were performed on synthetic data of known structures, and it was found that this evaluation function can distinguish the correctly reconstructed electron-density image from wrong ones when diffraction data of atomic resolution are available. An algorithm was established based on this evaluation function and applied in reconstructing the electron-density image from the synthetic data of known structures. The other evaluation function, which is based on the positivity of electron density and constrained power spectrum entropy maximization, was designed for cases where only diffraction data of rather limited resolution are available. Tests on the synthetic data indicate that this evaluation function may identify the correct phase set even for a data set with resolution as low as 3.5 angstrom. Though no algorithm for structure solution has been figured out based on the latter function, the results presented here provide a new perspective on the phase problem.
We firstly study the inclusion problem of 0 is an element of T(x) for an H-accretive operator introduced in [Yaping Fang, Nanjing Huang, H-accretive operators and resolvent operator technique for solving variational i...
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We firstly study the inclusion problem of 0 is an element of T(x) for an H-accretive operator introduced in [Yaping Fang, Nanjing Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647-653] in Banach spaces and obtain strong convergence theorems and weak convergence theorems. Simultaneously, we analyze the relations between m-accretive operators and H-accretive operators and give some numerical examples to explain main results. The main results presented in this paper mainly extend and improve the results of [Tomas Dominguez Benavides, Genaro Lopez Acedo, Hong-Kun Xu, Iterative solutions for zeros of accretive operators, Math. Nachr. 248-249 (2003) 62-71] and [Hong-Kun Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631-643] from m-accretive operators to H-accretive operators. (C) 2011 Elsevier Inc. All rights reserved.
In this paper, we introduce and consider some new systems of extended general variational inclusions involving seven different operators. Using the resolvent operator technique, we show that the new systems of extende...
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In this paper, we introduce and consider some new systems of extended general variational inclusions involving seven different operators. Using the resolvent operator technique, we show that the new systems of extended general variational inclusions are equivalent to the fixed point problems. This equivalent formulation is used to suggest and analyze some new iterative methods for this system of extended general variational inclusions. We also study the convergence analysis of the new iterative method under certain mild conditions. Several special cases are also discussed. Results obtained in this paper can be viewed as pure mathematical contribution to variational analysis.
Models of costs dependence on elements parameter deviation are being considered. Coefficients of external influences are being taken into account. A criterion of radio-electronic devices costs minimization was defined...
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ISBN:
(纸本)9789531841306
Models of costs dependence on elements parameter deviation are being considered. Coefficients of external influences are being taken into account. A criterion of radio-electronic devices costs minimization was defined. An algorithm of elements parameter selection under normal distribution law os submitted.
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