scholarly journals A Neural Network-Based Approach for Approximating Arbitrary Roots of Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 317
Author(s):  
Diogo Freitas ◽  
Luiz Guerreiro Lopes ◽  
Fernando Morgado-Dias
Keyword(s):  
Iterative Methods ◽  
Fundamental Problem ◽  
Iterative Algorithms ◽  
Rounding Errors ◽  
Suggested Approach ◽  
Simultaneous Iterative Methods ◽  
Complex Roots ◽  
Roots Of Polynomials ◽  
Comparative Results ◽  
The One

Finding arbitrary roots of polynomials is a fundamental problem in various areas of science and engineering. A myriad of methods was suggested to address this problem, such as the sequential Newton’s method and the Durand–Kerner (D–K) simultaneous iterative method. The sequential iterative methods, on the one hand, need to use a deflation procedure in order to compute approximations to all the roots of a given polynomial, which can produce inaccurate results due to the accumulation of rounding errors. On the other hand, the simultaneous iterative methods require good initial guesses to converge. However, Artificial Neural Networks (ANNs) are widely known by their capacity to find complex mappings between the dependent and independent variables. In view of this, this paper aims to determine, based on comparative results, whether ANNs can be used to compute approximations to the real and complex roots of a given polynomial, as an alternative to simultaneous iterative algorithms like the D–K method. Although the results are very encouraging and demonstrate the viability and potentiality of the suggested approach, the ANNs were not able to surpass the accuracy of the D–K method. The results indicated, however, that the use of the approximations computed by the ANNs as the initial guesses for the D–K method can be beneficial to the accuracy of this method.

scholarly journals Iterative methods for generalized split feasibility problems in Banach spaces

2017 ◽  
Vol 33 (1) ◽  
pp. 09-26
Author(s):  
QAMRUL HASAN ANSARI ◽  
◽  
AISHA REHAN ◽  
◽  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Split Feasibility Problems ◽  
Convergence Results ◽  
Split Feasibility

Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205–221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, SetValued Var. Anal., 23 (2015), 205–221].

scholarly journals RELIGION IN THOUGHT MURTADHA MUTHAHHARI

Tsaqofah ◽  
2020 ◽  
Vol 18 (02) ◽  
pp. 99
Author(s):  
Didin Komarudin Komarudin
Keyword(s):  
Content Analysis ◽  
Fundamental Problem ◽  
Religious Practice ◽  
Sociological Analysis ◽  
Religion And Science ◽  
Daily Lives ◽  
The One ◽  
And Behavior ◽  
The Relationship ◽  
Religious Actors

This writing is based on the background that religious formalism is increasingly becoming a fundamental problem. This is marked by the patterns and behavior of people who claim to be religious but there is no concrete implementation in their daily lives. This research was conducted to determine the concept of religion as a fitrah for humans as well as how religious beliefs are to the level of the relationship between religion and science according to Murtadha Motahhari. This research is a qualitative study that uses a sociological analysis approach, while the data in this study come from content analysis collected from various sources. , the level of religious belief, until people know God, the criticisms of Murtadha muthahhari which are an integral part of the life of the above figures to practice true religious values. Religion as human nature gives birth to the belief that religion is the only way to fulfill all needs, so that religion is not only a label or social formality but is able to become a guide in life and life. All religions teach goodness and peace, and no religion teaches violence. But sometimes there is violence in the name of religion because of a lack of understanding or a distortion of the source of religion itself. So that religion is sometimes used, and it seems that religion and religious practice are the opposite. So what is blamed on the concept of religion itself is actually the one who is wrong for religious actors.

scholarly journals Studying and evaluating the performance of pedestrian crossing facilities in Babil governorate

2019 ◽  
Vol 28 (3) ◽  
pp. 417-431
Author(s):  
Ali Dakhil ◽  
Dheyaa Alobaidi ◽  
Saba Shaheed
Keyword(s):  
Fundamental Problem ◽  
Health Department ◽  
Positive Effects ◽  
Pedestrian Bridges ◽  
Traffic Volumes ◽  
Interview Survey ◽  
The One ◽  
Questionnaire Method ◽  
Pedestrian Crossing ◽  
In Transit

Walking is one of the oldest means of mobility. It is an indispensable necessity to reach destinations despite the fact that walking or walking is one of everyday activities of man, which have positive effects on health, and activity on the one hand; vehicles cannot reach destinations only required by often walking from the other. The main problem address by the research is the random passage of the sieve and uncontrolled when it is most designs for the city’s road network have not addressed. This fundamental problem as well as the lack of a city to the safe facilities to cross the pedestrian. Therefore, this paper is a trial to study and analyze the current reality of crossing the sap then find solutions and treatments that reduce or limit the overlap between different traffic events and events crossing the pedestrian. Field data on the syllabic traffic volumes collected in all areas of the study (peak hour volume) and the photographic technique method. The study chose four areas to study the sap (60th Street, 40th Street, Al-Hussein, intersection circle at Babel Health Department), which are residential, commercial and educational zones, representing diversity in land use and scheme sidewalk and the design of the city of Hilla. The study attempted to show the state of lateral walks. The study also used the questionnaire method (interview survey) to determine the suitability of pedestrian bridges in transit and land transit. The study concluded that the area of Al-Hussein represents the highest traffic volumes of the sieve in addition to the lack of it the sidewalks in terms of absorption and quality and abuses. As well as the reluctance to use pedestrian bridges in transit in the area of 60th Street through high ground transit time, which necessitates the establishment of dual-step (fixed and mobile) – legislation and education through all means.

Numerical Methods I

2021 ◽  
Author(s):  
Boris Obsieger
Keyword(s):  
Numerical Methods ◽  
Computer Program ◽  
Iterative Methods ◽  
Error Propagation ◽  
Random Variables ◽  
Regression Analyses ◽  
Practical Application ◽  
Numeral Systems ◽  
Roots Of Polynomials ◽  
Digital Computers

Textbook of several universities. 2nd edition. The color edition is also available at Glasstree Bookstore. It is recommended for students. The series of books Numerical Methods is written primarily for students at technical universities, but also as a useful handbook for engineers, PhD students and scientists. This volume introduces the reader into numeral systems and representation of numbers in digital computers. Possibly the most important part of this book are descriptions of differences between constant and random variables, related types of errors and error propagation. These topics are supplemented with various types of regression analyses. Finally, direct and iterative methods for finding roots of polynomials are explained. Practical application is supported by 77 examples and 13 algorithms. For reasons of simplicity, algorithms are written in pseudo-code, so they can easily be included in any computer program.

On How the Generation of Lift Can Be Explained in a Closed Form Based on the Fundamental Conservation Equations

2020 ◽  
Author(s):  
Philipp Epple ◽  
Holger Babinsky ◽  
Michael Steppert ◽  
Manuel Fritsche
Keyword(s):  
Fluid Mechanics ◽  
Closed Form ◽  
Fundamental Problem ◽  
System Of Equations ◽  
Bernoulli Equation ◽  
Conservation Equations ◽  
Research Institutes ◽  
Conservation Principles ◽  
Newton’S Laws ◽  
The One

Abstract The generation of lift is a fundamental problem in aerodynamics and in general in fluid mechanics. The explanations on how lift is generated are often very incomplete or even not correct. Perhaps the most popular explanation of lift is the one with the Bernoulli equation and with the longer path over an airfoil as compared to the path below the airfoil, assuming the flow arrives at the same time at the trailing edge on both paths. This is an intuitive assumption, but no equation is derived from this assumption. In some explanations the Bernoulli equation is also complemented with Newton’s laws of motion. In other explanations Newton’s law is said to be the only explanation. Other explanations mention the Venturi suction effect to explain the generation of lift. In books of aerodynamics and on the homepage of well-known research institutes the explanations are, although better and partially correct, still very often incomplete. In this contribution the generation of lift is explained in a scientific way based on the conservation principles of mass, momentum and energy and how they have to be applied to close the system of equations in order to explain the generation of lift. The most common incomplete or incorrect explanations of lift are also analysed and it is explained why they are incomplete or wrong. In this work the generation of lift is explained based on the conservation equations. It is shown how and when they apply to the problem of lift generation and how the system of equations has to be closed.

The Conduct of ‘Post-Mortems’ on Concluded Field Trials

1976 ◽  
Vol 12 (2) ◽  
pp. 151-162 ◽  
Author(s):  
S. C. Pearce
Keyword(s):  
Iterative Methods ◽  
Environmental Variation ◽  
Field Trials ◽  
Recent Developments ◽  
The One ◽  
Alternative Designs ◽  
Working Out

SUMMARYThe design of field trials sometimes raises queries (which often go unanswered) about alternative designs and the best ways of allowing for environmental variation in the area allotted to the experiment. It is shown how recent developments in iterative methods for working out analyses of variance make possible the determination of error for systems of blocks other than the one actually used, and also for the row-and-column case. Some suggestions are also made for judging the error to be expected if plots were made larger.

scholarly journals CONTINUOUS PETRI NETS: EXPRESSIVE POWER AND DECIDABILITY ISSUES

2010 ◽  
Vol 21 (02) ◽  
pp. 235-256 ◽  
Author(s):  
LAURA RECALDE ◽  
SERGE HADDAD ◽  
MANUEL SILVA
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Expressive Power ◽  
Timed Petri Nets ◽  
Analysis And Synthesis ◽  
Continuous Petri Nets ◽  
Linear Differential ◽  
The One

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of the corresponding discrete model. The expected gains are twofold: improvements in complexity and in decidability. In the case of autonomous nets we prove that liveness or deadlock-freeness remain decidable and can be checked more efficiently than in Petri nets. Then we introduce time in the model which now behaves as a dynamical system driven by differential equations and we study it w.r.t. expressiveness and decidability issues. On the one hand, we prove that this model is equivalent to timed differential Petri nets which are a slight extension of systems driven by linear differential equations (LDE). On the other hand, (contrary to the systems driven by LDEs) we show that continuous timed Petri nets are able to simulate Turing machines and thus that basic properties become undecidable.

An Efficient Technique to Ensure the Logical Consistency of Interacting Knowledge Bases

1997 ◽  
Vol 06 (01) ◽  
pp. 27-36 ◽  
Author(s):  
Bertrand Mazure ◽  
Lakhdar Saïs ◽  
Éric Grégoire
Keyword(s):  
Local Search ◽  
Fundamental Problem ◽  
Real Life ◽  
Knowledge Bases ◽  
The Other ◽  
Logical Consistency ◽  
Complete Problem ◽  
Np Complete ◽  
The One ◽  
Cooperative Knowledge

In this paper, we address a fundamental problem in the formalization and implementation of cooperative knowledge bases: the difficulty of preserving consistency while interacting or combining them. Indeed, knowledge bases that are individually consistent can exhibit global inconsistency. This stumbling-block problem is an even more serious drawback when knowledge and reasoning are expressed using logical terms. Indeed, on the one hand, two contradictory pieces of information lead to global inconsistency under complete standard rules of deduction: every assertion and its contrary can be deduced. On the other hand, checking the logical consistency of a propositional knowledge base is an NP-complete problem and is often out of reach for large real-life applications. In this paper, a new practical technique to locate inconsistent interacting pieces of information is presented in the context of cooperative logical knowledge bases. Based on a recently discovered heuristic about the work performed by local search techniques, it can be applied in the context of large interacting knowledge bases.

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