Convergence Theory Research Articles

Convergence theory of efficient parametric iterative methods for solving the Yang-Baxter-like matrix equation

PurposeIn this study, we present a novel parametric iterative method for computing the polar decomposition and determining the matrix sign function.Design/methodology/approachThis method demonstrates exceptional efficiency, requiring only two matrix-by-matrix multiplications and one matrix inversion per iteration. Additionally, we establish that the convergence order of the proposed method is three and four, and confirm that it is asymptotically stable.FindingsIn conclusion, we extend the iterative method to solve the Yang-Baxter-like matrix equation. The efficiency indices of the proposed methods are shown to be superior compared to previous approaches.Originality/valueThe efficiency and accuracy of our proposed methods are demonstrated through various high-dimensional numerical examples, highlighting their superiority over established methods.

Exploring the Role of Symbolic Convergence Theory in Enhancing Group Cohesiveness and Decision Making: A Systematic Literature Review Study

Symbolic Convergence Theory describes group cohesiveness and decision-making influenced by symbolic convergence and rhetorical vision because they affect how group members understand and share common social values. This research aims to provide an overview of the implementation of Symbolic Convergence Theory in group communication, especially in cohesiveness and group decision-making. This research uses the Systematic Literature Review (SLR) method. This research systematically identifies and evaluates group cohesiveness and decision-making in several previous studies. However, along with the development of time and technology, direct and analog communication began to be less researched. Keywords: Symbolic Convergence Theory, group, cohesiveness, decision-making

Exploring the Theory of Preschool Skill Convergence Through a National Survey of Kindergarten Teachers

ABSTRACT Preschool effectiveness research consistently documents “fadeout” or “convergence” wherein initial preschool gains dissipate when students enter school. Most fadeout occurs in kindergarten, leading scholars to theorize about mechanisms that make kindergarten a “hotspot” for fadeout. Fielding a national survey of kindergarten teachers (n = 422), this study is the first to shed light on some of these theoretical propositions through the insights of kindergarten teachers themselves. Research Findings: Teachers report that kindergarten classrooms are heterogeneous in terms of school readiness skills and students who attended preschool often enter school near the top of their class. Kindergarten teachers report focusing instructional support on students near the bottom of the class, and consequently, see the differences between students that attended preschool and those that did not converge over the school year. Practice or Policy: This study provides practice-based insights from teachers on a commonly cited theory of preschool skill convergence. The findings buttress the need for future research that can test the specific mechanisms implicated.

Finite-time event-triggered tracking control for quadcopter attitude systems with zero compensation technology

This paper primarily investigates the event-triggered tracking control problem for quadcopter attitude systems, utilizing finite-time zero compensation technology. Unlike existing research results, a zero compensation technology is proposed to solve non-affine control input problems such as saturation, dead zones, and gaps. The command filtered compensation technology is used to solve ’differential explosion’ and filtering errors. A novel Tanh type filter and a neural network are employed to approximate virtual control signals and account for un-modeled dynamics, respectively. Moreover, the finite-time convergence theory is used to prove that the state, tracking error, and filtered error compensation signals in the entire closed-loop system converge to an arbitrarily small neighborhood of the equilibrium origin. Finally, the advantages of the proposed control algorithm in improving tracking accuracy and reducing communication load were demonstrated through simulation.

Pengaruh Kompetensi Kepribadian Guru Pendidikan Pancasila terhadap Karakter Tanggung Jawab Siswa SMP Negeri 1 Percut Sei Tuan

This study aims to determine that the personality competence of Pancasila Education teachers can affect the character of responsibility of SMPN 1 Percut Sei Tuan students. The theory used is convergence theory. This research uses quantitative correlation method. The period of research implementation is from June 11 to July 12, 2024. Data gathering methods were conducted through observation, interviews, and documentation. The tools utilized for data acquisition in this research included Likert Scale surveys and open-ended questionnaires based on random sampling. The study participants were selected using a random sampling approach from a defined population of 309 students from a total of class VIII and a total sample of 40 students, with 4 representatives from each class. The types of data in this study are primary and secondary data. The data analysis techniques used are correlation test, determination test, hypothesis testing using a Likert scale. Data analysis in this study uses statistical quantitative methods with product moment calculations. This is evidenced by the calculation of the correlation coefficient between variable x and variable y, it is known that the rcount value is 0.563. If this value is compared with the rtable value at a significant 5% with n = 40, then the rcount is equal to the provisions, if the rcount value is greater than the rtable (0.563> 0.312) then, it can be concluded that there is a significant influence on the influence of the personality competence of the Pancasila Education teacher on the character of student responsibility in class VIII of SMP Negeri 1 Percut Sei Tuan in the 2023/2024 school year.

Numerical analysis of a 1/2-equation model of turbulence

The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov–Prandtl 1-equation URANS model. In tests, the 1/2-equation model produced comparable velocity statistics to a full 1-equation model with lower computational complexity. There is little progress in the numerical analysis of URANS models due to the difficulties in treating the coupling between equations and the nonlinearities in highest-order terms. The numerical analysis herein on the 1/2-equation model has independent interest and is also a first numerical analysis step to address the couplings and nonlinearities in a full 1-equation model. This report develops a complete numerical analysis of the 1/2-equation model. Stability, convergence, and error estimates are proven for a semi-discrete and fully discrete approximation. Finally, numerical tests are conducted to validate the predictions of the convergence theory.

Multigrid Reduction‐In‐Time Convergence for Advection Problems: A Fourier Analysis Perspective

ABSTRACTA long‐standing issue in the parallel‐in‐time community is the poor convergence of standard iterative parallel‐in‐time methods for hyperbolic partial differential equations (PDEs), and for advection‐dominated PDEs more broadly. Here, a local Fourier analysis (LFA) convergence theory is derived for the two‐level variant of the iterative parallel‐in‐time method of multigrid reduction‐in‐time (MGRIT). This closed‐form theory allows for new insights into the poor convergence of MGRIT for advection‐dominated PDEs when using the standard approach of rediscretizing the fine‐grid problem on the coarse grid. Specifically, we show that this poor convergence arises, at least in part, from inadequate coarse‐grid correction of certain smooth Fourier modes known as characteristic components, which was previously identified as causing poor convergence of classical spatial multigrid on steady‐state advection‐dominated PDEs. We apply this convergence theory to show that, for certain semi‐Lagrangian discretizations of advection problems, MGRIT convergence using rediscretized coarse‐grid operators cannot be robust with respect to CFL number or coarsening factor. A consequence of this analysis is that techniques developed for improving convergence in the spatial multigrid context can be re‐purposed in the MGRIT context to develop more robust parallel‐in‐time solvers. This strategy has been used in recent work to great effect; here, we provide further theoretical evidence supporting the effectiveness of this approach.

The centrality of English as one legacy of Lau: An interest convergence theory analysis of Massachusetts policy for English Learners

ABSTRACT Using the theoretical framework of interest convergence, this document analysis explores the legacy of Lau v. Nichols as a gateway to instructional programs for classified English learners in the state of Massachusetts that maintain the hegemony of English as the primary goal of schooling. Findings reveal that interest convergence is an organizing principle for how instruction for classified ELs has historically been organized and delivered throughout Massachusetts as a move both toward and away from English-only instructional policy.

Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D

In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless of the singular perturbation parameter. Asymptotically optimal order error estimate in a H2 discrete norm is established for the corresponding WG solutions. Numerical tests are provided to verify the convergence theory.

ENHANCING CUSTOMER ACQUISITION THROUGH CREATIVE COMMUNICATION IN PERSONAL SELLING: A CASE STUDY OF PT TIRTA ASASTA DEPOK (PERSERODA)

This research aims to explore the role of communication creativity in personal selling strategies to increase the number of customers in the Marketing Team of the Regional Water Company Tirta Asasta Depok in 2024. The method is an exploratory case study. Primary data was collected through interviews and direct observations, while secondary data was gathered from literature, company documents, and previous research. The theoretical framework includes Computer-Mediated Communication, Social Exchange Theory, and Media Convergence Theory. The research findings show that communication creativity in personal selling involves utilizing media convergence tools such as laptops, WhatsApp, email, and Zoom to interact and negotiate with customers. This strategy is further enhanced by offering rewards, providing gifts, and using motivational narratives to build relationships. It also includes delivering more comfortable services with improved negotiation management and collaborating with local authorities to expand outreach. As communicators, neat and polite appearances, along with the use of "lip service" to create comfort and trust play significant roles. However, communication barriers were negative customer perceptions regarding new connection fees, public corporate image, and the skepticism toward government-owned enterprises. The findings indicate that creativity in communication can effectively enhance customer acquisition.

Convergence Rates for Identification of Robin Coefficient from Terminal Observations

This paper deals with the problem of identification of a Robin coefficient (also known as impedance coefficient) in a parabolic PDE from terminal observations of the temperature distributions. The problem is ill-posed in the sense that small perturbation in the observation may lead to a large deviation in the solution. Thus, in order to obtain stable approximations, we employ the Tikhonov-regularization. We propose a weak source condition motivated by the work of Engl and Zou (2000) and obtain a convergence rate of O(δ12)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\delta ^\\frac{1}{2})$$\\end{document}, where δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} is the noise level of the observed data. The obtained rate is better than some of the previous known rates. Moreover, the advantage of the proposed source condition is that the above mentioned convergence rate is obtained without the need for characterizing the range space of modelling operator and its Fréchet derivative, which is in contrast to the general convergence theory of Tikhonov-regularization for non linear operators.

On the linear convergence of additive Schwarz methods for the p-Laplacian

Abstract We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for these methods, empirical evidence from numerical experiments demonstrates a linear convergence rate. In this paper we narrow the gap between these theoretical and empirical results by presenting a novel convergence analysis. First, we present a new convergence theory for additive Schwarz methods written in terms of a quasi-norm. This quasi-norm exhibits behaviour akin to the Bregman distance of the convex energy functional associated with the problem. Secondly, we provide a quasi-norm version of the Poincaré–Friedrichs inequality, which plays a crucial role in deriving a quasi-norm stable decomposition for a two-level domain decomposition setting. By utilizing these key elements we establish the asymptotic linear convergence of additive Schwarz methods for the $p$-Laplacian.

Finite-Time Line-of-Sight Guidance-Based Path-Following Control for a Wire-Driven Robot Fish.

This paper presents an adaptive line-of-sight (LOS) guidance method, incorporating a finite-time sideslip angle observer to achieve precise planar path tracking of a bionic robotic fish driven by LOS. First, an adaptive LOS guidance method based on real-time cross-track error is presented. To mitigate the adverse effects of the sideslip angle on tracking performance, a finite-time observer (FTO) based on finite-time convergence theory is employed to observe the time-varying sideslip angle and correct the target yaw. Subsequently, classical proportional-integral-derivative (PID) controllers are utilized to achieve yaw tracking, followed by static and dynamic yaw angle experiments for evaluation. Finally, the yaw-tracking-based path-tracking control strategy is applied to the robotic fish, whose motion is generated by an improved central pattern generator (CPG) and equipped with a six-axis inertial measurement unit for real-time swimming direction. Quantitative comparisons in tank experiments validate the effectiveness of the proposed method.

On the nature of Bregman functions

Let C⊂Rn be convex, compact, with nonempty interior and h be Legendre with domain C, continuous on C. We prove that h is Bregman if and only if it is strictly convex on C and C is a polytope. This provides insights on sequential convergence of many Bregman divergence based algorithm: abstract compatibility conditions between Bregman and Euclidean topology may equivalently be replaced by explicit conditions on h and C. This also emphasizes that a general convergence theory for these methods (beyond polyhedral domains) would require more refinements than Bregman's conditions.

Spatiotemporal evolution pattern and heterogeneity of resource-based city resilience in China

Resource-based cities (RBCs) encompass the east, middle, and west of China, covering an important economic hinterland. The improvement of RBC resilience can significantly impact the overall resilience of cities in China. This study analyzes the spatial characteristics and overall evolution trend of four types of RBCs based on regional differences and convergence theory. The results vivid showed sustainable development positively influenced growing-type RBCs also showed that the overall RBC resilience coupling coordination degree improved throughout the study period (2009–2019), and that the evolution of RBC resilience demonstrated good convergence characteristics. Furthermore, a distinct gap is evident between high resilience-level growing RBCs and relatively low-level regenerative RBCs. All RBCs will eventually converge to the third level with a higher level of coupling coordination. However, compared with the traditional Markov chain, the transition probability of the spatial Markov chain is reduced due to the influence of surrounding cities. Thus, policies are given.

Impact of Social Media on Cultural Identity in Urban Youth

Purpose: The aim of the study was to assess the impact of social media on cultural identity in urban youth. Materials and Methods: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: Social media platforms serve as significant spaces where urban youth engage, express, and negotiate their cultural identities. These platforms provide access to a diverse range of cultural expressions, facilitating the blending and reshaping of traditional and modern cultural elements. Studies have shown that social media influences urban youth by offering a sense of community and belonging, where they can connect with like-minded peers globally, thus fostering a globalized cultural perspective. However, this exposure also poses challenges, such as cultural homogenization and the potential loss of distinct local cultural identities. Additionally, the curated nature of social media content often promotes idealized cultural norms, influencing youth to conform to certain stereotypes and societal expectations. Despite these challenges, social media remains a powerful tool for cultural expression and identity formation, enabling urban youth to navigate and redefine their cultural landscapes in dynamic and innovative ways. Implications to Theory, Practice and Policy: Social identity theory, uses and gratifications theory and cultural convergence theory may be used to anchor future studies on assessing the impact of social media on cultural identity in urban youth. Practically, there is a pressing need for digital literacy programs that educate youth on critical engagement with social media. From a policy perspective, integrating cultural education into school curricula is essential.

Dynamically accelerating the power iteration with momentum

AbstractIn this article, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be applied to real diagonalizable matrices, is provably convergent with acceleration in the symmetric case, and does not require a priori spectral knowledge. We review and extend background results on previously developed static momentum accelerations for the power iteration through the connection between the momentum accelerated iteration and the standard power iteration applied to an augmented matrix. We show that the augmented matrix is defective for the optimal parameter choice. We then present our dynamic method which updates the momentum parameter at each iteration based on the Rayleigh quotient and two previous residuals. We present convergence and stability theory for the method by considering a power‐like method consisting of multiplying an initial vector by a sequence of augmented matrices. We demonstrate the developed method on a number of benchmark problems, and see that it outperforms both the power iteration and often the static momentum acceleration with optimal parameter choice. Finally, we present and demonstrate an explicit extension of the algorithm to inverse power iterations.

Board expertise diversity and firm performance in sub-Saharan Africa: do firm age and size matter?

Our study delved into an analysis of 128 public companies in Ghana, Kenya, and Nigeria to explore the influence of diversified board expertise on firm performance. We also investigated the impact of firm size and age on this relationship. Our results indicate that a varied blend of professional experts on corporate boards significantly boosts a company's ROA, although there is no significant effect when Tobin's Q measures firm performance. Nevertheless, we discovered that combining firm size and age negatively impacts the correlation between board expertise diversity and firm performance. Our findings support the significance of integrating agency, resource dependence, and convergence theories, implying that businesses can improve their financial performance by including an appropriate mix of expertise on their boards, especially for relatively younger small-sized firms. In contrast, more prominent and ageing firms may not see the same financial benefits. Consequently, we recommend that corporate executives and practitioners consider implementing board expertise diversity to enhance their firms' financial performance.

Convergent least-squares optimization methods for variational data assimilation

Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is in numerical weather prediction where a previous forecast and atmospheric observations are used to obtain the initial conditions for a numerical weather forecast. In four-dimensional variational data assimilation (4D-Var), the problem is formulated as a nonlinear least-squares problem, usually solved using a variant of the classical Gauss-Newton (GN) method. However, we show that GN may not converge if poorly initialized. In particular, we show that this may occur when there is greater uncertainty in the background information compared to the observations, or when a long time-window is used in 4D-Var allowing more observations. The difficulties GN encounters may lead to inaccurate initial state conditions for subsequent forecasts. To overcome this, we apply two convergent GN variants (line search and regularization) to the long time-window 4D-Var problem and investigate the cases where they locate a more accurate estimate compared to GN within a given budget of computational time and cost. We show that these methods are able to improve the estimate of the initial state, which may lead to a more accurate forecast. Highlights Poor initialization of Gauss-Newton method may result in failure to converge. Safeguarded Gauss-Newton improves initial state estimate within limited time/cost. Results using twin experiments with long time-window and chaotic Lorenz models. Apply state of the art least-squares convergence theory to data assimilation. Improvements to initial state estimate may lead to a more accurate forecast.

Finite-Time Convergence Guidance Law for Hypersonic Morphing Vehicle

Aiming at the interception constraint posed by defensive aircrafts against hypersonic morphing vehicles (HMVs) during the terminal guidance phase, this paper designed a guidance law with the finite-time convergence theory and control allocation methods based on the event-triggered theory, achieving evasion of the defensive aircraft and targeting objectives for a morphing vehicle in the terminal guidance phase. Firstly, this paper established the aircraft motion model; the relative motion relationships between HMV, defensive aircraft, and target; and the control equations for the guidance system. Secondly, a guidance law with finite-time convergence was designed, establishing a controller with the angle between the aircraft–target–defense aircraft triplet as the state variable and lift as the control variable. By ensuring the angle was non-zero, the aircraft maintained a certain relative distance from the defense aircraft, achieving evasion of interception. The delay characteristic of the aircraft’s flight controller was considered, analyzing its delay stability and applying control compensation. Thirdly, a multi-model switching control allocation method based on an event-triggered mechanism was designed. Optimal attack and bank angles were determined based on acceleration control variables, considering different sweep angles. Finally, simulations were conducted to validate the effectiveness and robustness of the designed guidance laws.