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This paper proposes new iterative algorithms by using the generalized viscosity implicit midpoint rule in Banach space, which is also a symmetric space. Then, this paper obtains strong convergence conclusions. Moreover, the results generalize the related conclusions of some researchers. Finally, this paper provides some examples to verify these conclusions. These conclusions further extend and enrich the relevant theory of symmetric space. [ABSTRACT FROM AUTHOR]

In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm's effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems. [ABSTRACT FROM AUTHOR]

This work focuses on linear system identification problems in the framework of the Wiener filter. Specifically, it addresses the challenging identification of systems characterized by impulse responses of long length, which poses significant difficulties due to the existence of large parameter space. The proposed solution targets a dimensionality reduction of the problem by involving the decomposition of a fourth-order tensor, using low-rank approximations in conjunction with the nearest Kronecker product. In addition, the rank of the tensor is controlled and limited to a known value without involving any approximation technique. The final estimate is obtained based on a combination of four (shorter) optimal filters, which are alternatively iterated. As a result, the designed iterative Wiener filter outperforms the traditional counterpart, being more robust to the accuracy of the statistics' estimates and/or noisy conditions. In addition, simulations performed in the context of acoustic echo cancellation indicate that the proposed iterative Wiener filter that exploits this fourth-order tensor decomposition achieves better performance as compared to some previously developed solutions based on lower decomposition levels. This study could further lead to the development of computationally efficient tensor-based adaptive filtering algorithms. [ABSTRACT FROM AUTHOR]

The timeliness of order deliveries seriously impacts customers' evaluation of logistics services and, hence, has increasingly received attention. Due to the diverse and large quantities of orders under the background of electronic commerce, how to pick orders efficiently while also adapting these features has become one of the most challenging problems for distribution centers. However, previous studies have not accounted for the differences in the stochastic characteristics of order generation, which may lead to asymmetric optimization problems. With this in mind, a new asymmetric polling-based model that assumes the varying stochastic characteristics to analyze such order picking systems is put forward. In addition, two important indicators of the system, mean queue length (MQL) and mean waiting time (MWT), are derived by using probability-generating functions and the embedded Markov chain. Then, simulation experiments and a comparison of the numerical and theoretical results are conducted, showing the usefulness and practicalities of the proposed model. Finally, the paper discusses the characteristics of the novel order picking system and the influence of the MQL and MWT on it. [ABSTRACT FROM AUTHOR]

In the paper, we determine the period of an n-dimensional nonlinear dynamical system by using a derived formula in an (n + 1)-dimensional augmented space. To form a periodic motion, the periodic conditions in the state space and nonlinear first-order differential equations constitute a special periodic problem within a time interval with an unknown length. Two periodic problems are considered: (a) boundary values are given and (b) boundary values are unknown. By using the shape functions, a boundary shape function method (BSFM) is devised to obtain an initial value problem with the initial values of the new variables given. The unknown terminal values of the new variables and period are determined by two iterative algorithms for the case (a) and one iterative algorithm for the case (b). The periodic solutions obtained from the BSFM satisfy the periodic conditions automatically. For the numerical example, the computed order of convergence displays the merit of the BSFM. For the sake of comparison, the iterative algorithms based on the shooting method for cases (a) and (b) were developed by directly implementing the Poincaré map into the fictitious time-integration method to determine the period. The BSFM is better than the shooting method in terms of convergence speed, accuracy, and stability. [ABSTRACT FROM AUTHOR]

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions. [ABSTRACT FROM AUTHOR]

In the present paper, an iterative algorithm is proposed for solving the generalized (P , Q) -reflexive solution group of a system of quaternion matrix equations ∑ l = 1 M (A l s X l B l s + C l s X l ˜ D l s) = F s , s = 1 , 2 , ... , N . A generalized (P , Q) -reflexive solution group, as well as the least Frobenius norm generalized (P , Q) -reflexive solution group, can be derived by choosing appropriate initial matrices, respectively. Moreover, the optimal approximate generalized (P , Q) -reflexive solution group to a given matrix group can be derived by computing the least Frobenius norm generalized (P , Q) -reflexive solution group of a reestablished system of matrix equations. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature. [ABSTRACT FROM AUTHOR]

The problem of determining the position of the lidar with optimal accuracy is relevant in various fields of application. This is an important task of robotics that is widely used as a model when planning the route of vehicles, flight control systems, navigation systems, machine learning, and managing economic efficiency, a study of land degradation processes, planning and control of agricultural production stages, land inventory to evaluations of the consequences of various environmental impacts. The paper provides a detailed analysis of the proposed parallelization algorithm for solving the problem of determining the current position of the lidar. To optimize the computing process in order to accelerate and have the possibility of obtaining a real-time result, the OpenMP parallel computing technology is used. It is also possible to significantly reduce the computational complexity of the successive variant. A number of numerical experiments on the multi-core architecture of modern computers have been carried out. As a result, it was possible to accelerate the computing process about eight times and achieve an efficiency of 0.97. It is shown that a special difference in time of execution of a sequential and parallel algorithm manages to increase the number of measurements of lidar and iterations, which is relevant in simulating various problems of robotics. The obtained results can be substantially improved by selecting a computing system where the number of cores is more than eight. The main areas of application of the developed method are described, its shortcomings and prospects for further research are provided. [ABSTRACT FROM AUTHOR]

The problem of effective intellectual analysis in the case of handling short datasets is topical in various application areas. Such problems arise in medicine, economics, materials science, science, etc. This paper deals with a new additive input-doubling method designed by the authors for processing short and very short datasets. The main steps of the method should include the procedure of data augmentation within the existing dataset both in rows and columns (without training), the use of nonlinear SVR to implement the training procedure, and the formation of the result based on the author's procedure. The authors show that the developed data augmentation procedure corresponds to the principles of axial symmetry. The training and application procedures of the method developed are described in detail, and two algorithmic implementations are presented. The optimal parameters of the method operation were selected experimentally. The efficiency of its work during the processing of short datasets for solving the prediction task was established experimentally by comparison with other methods of this class. The highest prediction accuracy based on both proposed algorithmic implementations of a method among all of the investigated ones was defined. The main areas of application of the developed method are described, and its shortcomings and prospects of further research are given. [ABSTRACT FROM AUTHOR]

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of L p → (R d) are also given. [ABSTRACT FROM AUTHOR]

Inverse planning is a method of radiotherapy treatment planning where the care team begins with the desired dose distribution satisfying prescribed clinical objectives, and then determines the treatment parameters that will achieve it. The variety in symmetry, form, and characteristics of the objective functions describing clinical criteria requires a flexible optimization approach in order to obtain optimized treatment plans. Therefore, we introduce and discuss a nonlinear optimization formulation called the split common coincidence point problem (SCCPP). We show that the SCCPP is a suitable formulation for the inverse planning optimization problem with the flexibility of accommodating several biological and/or physical clinical objectives. Also, we propose an iterative algorithm for approximating the solution of the SCCPP, and using Bregman techniques, we establish that the proposed algorithm converges to a solution of the SCCPP and to an extremum of the inverse planning optimization problem. We end with a note on useful insights on implementing the algorithm in a clinical setting. [ABSTRACT FROM AUTHOR]