scholarly journals On an iterative process for the grid conjugation problem with iterations on the boundary of the solution discontinuity

2019 ◽  
Vol 21 (3) ◽  
pp. 329-342
Author(s):  
Fedor V. Lubyshev ◽  
Mahmut E. Fairuzov
Keyword(s):  
Iterative Process ◽  
Discontinuous Solution ◽  
Iteration Process ◽  
Initial Approximation ◽  
Discontinuous Coefficients ◽  
Theory And Practice ◽  
Difference Approximation ◽  
Boundary Problems ◽  
Equations Of Mathematical Physics ◽  
Grid Solution

An iterative process for the grid problem of conjugation with iterations on the boundary of the discontinuity of the solution is considered. Similar grid problem arises in difference approximation of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions. The study of iterative processes for the states of such problems is of independent interest for theory and practice. The paper shows that the numerical solution of boundary problems of this type can be efficiently implemented using iterations on the inner boundary of the grid solution discontinuity in combination with other iterative methods for nonlinearities separately in each of the grid subregions. It can be noted that problems for states of controlled processes described by equations of mathematical physics with discontinuous coefficients and solutions arise in mathematical modeling and optimization of heat transfer, diffusion, filtration, elasticity theory, etc. The proposed iterative process reduces the solution of the initial grid boundary problem for a state with a discontinuous solution to a solution of two special boundary problems in two grid subdomains at every fixed iteration. The convergence of the iteration process in the Sobolev grid norms to the unique solution of the grid problem for each initial approximation is proved.

Some convergence results of M iterative process in Banach spaces

2019 ◽  
pp. 2150017 ◽  
Author(s):  
Kifayat Ullah ◽  
Faiza Ayaz ◽  
Junaid Ahmad
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Convergence Results

In this paper, we prove some weak and strong convergence results for generalized [Formula: see text]-nonexpansive mappings using [Formula: see text] iteration process in the framework of Banach spaces. This generalizes former results proved by Ullah and Arshad [Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018) 187–196].

scholarly journals Fractals As Triggers For Exploratory Statistical Analysis of Clinical Pharmacological Data

2013 ◽  
pp. 53-57
Author(s):  
S.K. Kulishov ◽  
O.M. Iakovenko
Keyword(s):  
Data Analysis ◽  
Statistical Analysis ◽  
Iterative Process ◽  
Iteration Process ◽  
Underlying Structure ◽  
Anova Analysis ◽  
Parametric Data ◽  
Pharmacological Data ◽  
Selection Of

Proposed and tested an algorithm of using principles of Cantor, von Koch sets for exploratory fractals clinical pharmacological data analysis. The algorithm is based on the grouping data, formation of categorical variabilities in the form of subgroups as iteration process as for receiving Cantor, von Koch sets. It boils down to: selection of informative numerical dependent variabilities; transformation these informative numerical dependent variabilities to new categorical variabilities; formation categorical variabilities in the form of subgroups as a result of an iterative process as for Cantor, von Koch sets; statistical analysis of the data; determination of the distribution of variabilities; transformations that may be normalize from non-normal data; ANOVA - analysis of variance parametric data or nonparametric equivalent of ANOVA - Kruskal-Wallis testing; formulation of the conclusion. Our algorithm of using Cantor, von Koch sets principles for Exploratory Fractals Data Analysis of clinical pharmacological data will help maximize insight, uncover underlying structure, extract important variables, develop models and determine optimal factor settings.

Evolution of framework foresight

foresight ◽  
2020 ◽  
Vol 22 (5/6) ◽  
pp. 643-651
Author(s):  
Andy Hines
Keyword(s):  
Iterative Process ◽  
Design Methodology ◽  
Theory And Practice ◽  
Teaching Tool ◽  
Established Method ◽  
Content Type ◽  
Strategic Approach ◽  
The Future ◽  
Unique Approach ◽  
Practical Implications

Purpose The organization’s core approach to exploring and influencing the future, Framework Foresight, emerged from piecemeal roots in the 1990s to an established method circa 2013. Since then, it has evolved from primarily a teaching tool to a project methodology in its own right. The purpose of this paper is to explore the iterative process that has emerged in which teaching and practice inform and advance one another. Design/methodology/approach Innovations in technique will be highlighted and illustrated by commentary from project experience. The piece will be providing readers with a birds-eye view into the evolution of a foresight method in both theory and practice. Findings The continuous iteration between theory and practice, or the classroom and the client world, provides an excellent means to advance the teaching and practice of foresight. Significant changes include three horizons, inputs, drivers, archetypes, rating scenarios and strategic approach. Practical implications This paper suggests that closer relationships between academia and the external/client world provide practical benefit by improving teaching and providing more innovative approaches for clients. Originality/value The description of the development of this unique approach to doing foresight work provides an example for other programs or firms to emulate.

The Iterative Process of Legitimacy-Building in Hybrid Organizations

2021 ◽  
pp. 009539972110551
Author(s):  
Christian Rosser ◽  
Sabrina A. Ilgenstein ◽  
Fritz Sager
Keyword(s):  
Iterative Process ◽  
Mutual Influence ◽  
Analytical Framework ◽  
Theory And Practice ◽  
Hybrid Organizations ◽  
Moral Legitimacy ◽  
Normative Evaluation ◽  
Management Literature ◽  
Administrative Theory ◽  
Swiss Institute

Hybrid organizations face the fundamental challenge of building legitimacy. To deal with this challenge in administrative theory and practice, we apply an analytical framework following an organizational logic of legitimacy building to an exemplary case of hybridity—the Swiss Institute for Translational and Entrepreneurial Medicine. Our framework application illustrates that pragmatic legitimacy (i.e., establishing instrumental value) must be built before moral legitimacy (i.e., fostering normative evaluation) and cognitive legitimacy (i.e., creating comprehensibility), followed by an iterative process of mutual influence between the legitimacy forms. Originating in the management literature, the framework promises new insights for public administration research on hybrids.

scholarly journals Fixed Point Approximation for a Class of Generalized Nonexpansive Mappings in Hadamard Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Akbar Ali Khan ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Hadamard Space ◽  
Point Approximation ◽  
Convergence Results

In this paper, we establish strong and Δ convergence results for mappings satisfying condition B γ , μ through a newly introduced iterative process called JA iteration process. A nonlinear Hadamard space is used the ground space for establishing our main results. A novel example is provided for the support of our main results and claims. The presented results are the good extension of the corresponding results present in the literature.

scholarly journals On weak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in Banach space

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1699-1710
Author(s):  
Hukmi Kiziltunc ◽  
Yunus Purtas
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Process ◽  
Iteration Process ◽  
Nonempty Closed Convex Subset ◽  
Weak And Strong Convergence ◽  
New Class ◽  
Convergence Results ◽  
Definition Of

In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

AN ITERATIVE SCHEME FOR FIXED POINT PROBLEMS

2021 ◽  
Vol 10 (5) ◽  
pp. 2295-2316
Author(s):  
F. Akutsah ◽  
O. K. Narain ◽  
K. Afassinou ◽  
A. A. Mebawondu
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Examples ◽  
Convergence Results ◽  
The Stability

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm.

scholarly journals TWO-STAGE GRID METHOD OF SOLUTION OF BOUNDARY PROBLEMS OF STRUCTURAL MECHANICS WITH THE USE OF DISCRETE HAAR BASIS

2017 ◽  
Vol 13 (1) ◽  
pp. 69-85
Author(s):  
Marina L. Mozgaleva
Keyword(s):  
Three Dimensional ◽  
Initial Approximation ◽  
Grid Method ◽  
Coarse Grid ◽  
Discrete Problem ◽  
Two Stage ◽  
Boundary Problems ◽  
Fine Grid ◽  
Haar Basis ◽  
Dimensional Boundary

The distinctive paper is devoted to development of two-stage numerical method. At the first stage, the discrete problem is solved on a coarse grid, where the number of nodes in each direction is the same and is a pow-er of 2. Then the number of nodes in each direction is doubled and the resulting solution on a coarse grid using a discrete Haar basis is defined at the nodes of the fine grid as the initial approximation. At the second stage, we ob-tain a solution in the nodes of the fine grid using the most appropriate iterative method,. Test examples of the solu-tion of one-dimensional, two-dimensional and three-dimensional boundary problems are under consideration

scholarly journals An approach for constructing one-point iterative methods for solving nonlinear equations of one variable

2015 ◽  
pp. 298-306
Author(s):  
А.Н. Громов
Keyword(s):  
Singular Point ◽  
Convergence Rate ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Iterative Process ◽  
Initial Approximation ◽  
Higher Order ◽  
Convergence Criterion ◽  
Real Roots ◽  
Transcendental Equations

Предложен подход к построению одноточечных итерационных методов для решения нелинейных уравнений одного переменного. Подход основан на использовании понятия полюса в качестве особой точки и на применении критерия сходимости Коши. Показано, что такой подход приводит к новым итерационным процессам высшего порядка, которые имеют более широкую область сходимости по сравнению с известными методами. Доказаны теоремы сходимости и получены оценки скорости сходимости. Для многочленов, имеющих только действительные корни, итерационный процесс сходится для любого начального приближения. В общем случае для действительных корней трансцендентных уравнений сходимость имеет место при выборе начального приближения в окрестности корня. An approach for constructing one-point iterative methods for solving nonlinear equations of one variable is proposed. This approach is based on the concept of a pole as a singular point and on using Cauchy's convergence criterion. It is shown that such an approach leads to new iterative processes of higher order with larger convergence domains compared to the known iterative methods. Convergence theorems are proved and convergence rate estimates are obtained. For polynomials having only real roots, the iterative process converges for any initial approximation to the sought root. Generally, in the case of real roots of transcendental equations, the convergence takes place when an initial approximation is chosen near the sought root.

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