In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CS...
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In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings.
Finding iterative algorithms to approximate fixed points for nonexpansive mappings is a very, active topic in a number of mathematical and engineering areas, in particular, in image recovery and signal processing. Con...
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ISBN:
(纸本)9781424420957
Finding iterative algorithms to approximate fixed points for nonexpansive mappings is a very, active topic in a number of mathematical and engineering areas, in particular, in image recovery and signal processing. Considerable research efforts have been devoted to the study of this area in recent years. By now, there already exist some algorithms, but they are not quite enough to deal with problems of finding common fixed points of infinite nonexpansive mappings. In this paper, a more general form of iterative algorithm is introduced which is proved to be strongly convergent to common fixed point of infinite nonexpansive mappings in a real strictly convex and uniformly smooth Banach space by using sonic new techniques.
iterative algorithm for solution of magnetic field integral equation for electric current density on the surface of air radar object of resonant sizes with complex shape is considered. Features of developed numerical ...
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ISBN:
(纸本)9781479968640
iterative algorithm for solution of magnetic field integral equation for electric current density on the surface of air radar object of resonant sizes with complex shape is considered. Features of developed numerical algorithm are discussed, its convergence is investigated. Comparison of calculation results of the test object radar cross section obtained using different methods are carried out.
Model updating should be correlated with experimental data to ensure that it models the dynamics of the real structure and the updated model predicts the dynamics of a structure more accurately. Considering that the i...
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Model updating should be correlated with experimental data to ensure that it models the dynamics of the real structure and the updated model predicts the dynamics of a structure more accurately. Considering that the iterative methods for model updating have aroused little public attention, this paper studies an iterative algorithm for quadratic model updating problems which can incorporate the measured modal data into the finite element model to produce an adjusted finite element model on the mass, gyroscopic and stiffness matrices that closely match the experimental modal data. By this method, the best approximation symmetric and skew-symmetric solutions can be obtained by choosing a convergence factor. Numerical example shows that the introduced iterative algorithm is quite efficient. (C) 2011 Elsevier Inc. All rights reserved.
The article presents a modification of the algorithm for the inverse problem of electrocardiography originally proposed in [6]. The modification is intended to improve the computation accuracy and to reduce the comput...
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We propose a simple iterative(SI)algorithm for the maxcut problem through fully using an equivalent continuous *** does not need rounding at all and has advantages that all subproblems have explicit analytic solutions...
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We propose a simple iterative(SI)algorithm for the maxcut problem through fully using an equivalent continuous *** does not need rounding at all and has advantages that all subproblems have explicit analytic solutions,the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient *** experiments on G-set demonstrate the *** particular,the ratios between the best cut values achieved by SI and those by some advanced combinatorial algorithms in[***.,248(2017),365-403]are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.
A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the ...
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A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the approximate solutions of the generalized mixed equilibrium problems (GMEP) and bilevel generalized mixed equilibrium problems (BGMEP) involving set-valued mappings is introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions. By using auxiliary principle technique, new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP are suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithms are proved under quite mild assumptions. These results are new and generalize some recent results in this field.
In this paper, we consider two iterative algorithms for the Sylvester- conjugate matrix equation AV + BW = E (V) over barF + C and AV + B (W) over bar = E (V) over barF + C. When these two matrix equations are consist...
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In this paper, we consider two iterative algorithms for the Sylvester- conjugate matrix equation AV + BW = E (V) over barF + C and AV + B (W) over bar = E (V) over barF + C. When these two matrix equations are consistent, for any initial matrices the solutions can be obtained within finite iterative steps in the absence of round off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. Two numerical examples are given to illustrate the effectiveness of the proposed method. (C) 2013 Elsevier Ltd. All rights reserved.
In recent years, a large number of tram-tracks have been constructed in typical soft soil area of China. Infrastructure defects due to the differential foundation settlement are serious issues in this area. To ensure ...
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In recent years, a large number of tram-tracks have been constructed in typical soft soil area of China. Infrastructure defects due to the differential foundation settlement are serious issues in this area. To ensure the operation safety of the tram, the influence of different infrastructure defects on the dynamic response of the tram-track system has been investigated in this paper. A dynamic model of a five-module 100% low-floor tram vehicle coupled with a slab track system is developed based on a finite element (FE) method and multibody kinematics. The articulation between different vehicle modules, the wheel-rail nonlinear contact, pad failures, and a cavity in the subgrade have been taken into account in this model. The dynamic response of the vehicle-track coupling system to different operation speeds and infrastructure defects are calculated. Results indicate that the vibration energy of the vehicle body is mainly distributed in the frequency range below 1.5 Hz. This frequency range should be paid special attention in the durability design for the vehicle structure. When the number of the failure pads is larger than 3, the pad failure in tram-track has significant influence on the system dynamic response. A cavity in subgrade has a limited effect on high frequency vibrations (above 100 Hz) of the rail, while the low frequency vibrations (below 75 Hz) of the rail can be obviously increased by cavities in subgrade. The model can be used in the optimization of suspension parameters and the tram vehicle-track coupled vibration analysis.
Pairwise comparison matrix (PCM) is an important tool to rank items by deriving priorities and has been used in various applications. Though large-scale sparse PCMs appear frequently in today's big data environmen...
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Pairwise comparison matrix (PCM) is an important tool to rank items by deriving priorities and has been used in various applications. Though large-scale sparse PCMs appear frequently in today's big data environment, it is hard for existing prioritization methods to handle large-scale sparse PCMs efficiently due to the curse of dimensionality. The goal of this article is to propose a new algorithm, bipartite graph iterative method (BGIM), to derive priorities from large-scale sparse PCMs. We first extended graph representations of PCMs to bipartite graphs. A transition matrix was induced by resource allocation on the bipartite graph. Finally, an iterative algorithm was designed to calculate priorities. The theoretical properties of the BGIM were analyzed to show its ability to derive priorities from large-scale sparse PCMs. Two experiments were conducted to validate the proposed approach. The numerical examples indicated that the BGIM can deal with traditional decision problems and derive reliable priorities with minimum Euclidean distance (ED) and minimum violation (MV) among the tested methods. The simulation examples suggested that the BGIM can not only derive reliable priorities from large-scale sparse PCMs but also require the least computation time compared with eight prioritization approaches. To demonstrate its applicability to real-world large-scale problems, we applied the BGIM to rank movies using MovieLens dataset with more than 100,000 ratings for 9125 movies. The results showed that the BGIM was the fastest approach and obtained the best ranking among the average ratings and the five prioritization methods.
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