The Experts below are selected from a list of 87 Experts worldwide ranked by ideXlab platform
Xiaohong Shi - One of the best experts on this subject based on the ideXlab platform.
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the Iteration Function on netpad
International Conference on Computer Science and Education, 2019Co-Authors: Jie Wang, Yongsheng Rao, Ruxian Chen, Hao Guan, Ying Wang, Xiaohong ShiAbstract:Iteration is a special graphic transformation similar to the recursive algorithm in programs, which can effectively solve some specific mathematical problems. At present, most dynamic geometry systems(DGS) have the Iteration Function, which meets the demand of teaching. NetPad, one of the DGSs, has optimized the Iteration Function on the basis of other sketchpads. This paper introduces the Iteration Function of NetPad. It provides the implicit Iteration, random color hierarchy of each Iteration object, trajectory Iteration and Iteration of Iteration. Through teaching cases, the superiority of NetPad in Iteration Function is verified.
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ICCSE - The Iteration Function on NetPad
2019 14th International Conference on Computer Science & Education (ICCSE), 2019Co-Authors: Jie Wang, Yongsheng Rao, Ruxian Chen, Hao Guan, Ying Wang, Xiaohong ShiAbstract:Iteration is a special graphic transformation similar to the recursive algorithm in programs, which can effectively solve some specific mathematical problems. At present, most dynamic geometry systems(DGS) have the Iteration Function, which meets the demand of teaching. NetPad, one of the DGSs, has optimized the Iteration Function on the basis of other sketchpads. This paper introduces the Iteration Function of NetPad. It provides the implicit Iteration, random color hierarchy of each Iteration object, trajectory Iteration and Iteration of Iteration. Through teaching cases, the superiority of NetPad in Iteration Function is verified.
Ramandeep Behl - One of the best experts on this subject based on the ideXlab platform.
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an Iteration Function having optimal eighth order of convergence for multiple roots and local convergence
Mathematics, 2020Co-Authors: Ramandeep Behl, Ioannis K Argyros, Michael Argyros, Mehdi Salimi, Arwa Jeza AlsolamiAbstract:In the study of dynamics of physical systems an important role is played by symmetry principles. As an example in classical physics, symmetry plays a role in quantum physics, turbulence and similar theoretical models. We end up having to deal with an equation whose solution we desire to be in a closed form. But obtaining a solution in such form is achieved only in special cases. Hence, we resort to iterative schemes. There is where the novelty of our study lies, as well as our motivation for writing it. We have a very limited literature with eighth-order convergent Iteration Functions that can handle multiple zeros m≥1. Therefore, we suggest an eighth-order scheme for multiple zeros having optimal convergence along with fast convergence and uncomplicated structure. We develop an extensive convergence study in the main theorem that illustrates eighth-order convergence of our scheme. Finally, the applicability and comparison was illustrated on real life problems, e.g., Van der Waal’s equation of state, Chemical reactor with fractional conversion, continuous stirred reactor and multi-factor problems, etc., with existing schemes. These examples further show the superiority of our schemes over the earlier ones.
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an optimal Iteration Function for multiple zeros with eighth order convergence
THE 9TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL METHODS (ICCM2018), 2018Co-Authors: Ramandeep Behl, Ali Saleh AlshomraniAbstract:Over the past several years, many scholars have attempted to construct higher-order schemes for locatingmultiple solutions of a univariate Function having known multiplicity m >1. But till date, we have a very limitedliterature (only four research articles) of eighth-order convergence Iteration Functions for multiple zeros. The primarycontribution of this study is to propose an optimal eighth-order scheme for multiple zeros having simple andcompact body structure with faster convergence. An extensive convergence analysis is also present with the maintheorem which clearly show the eighth-order convergence of propose Iteration scheme. Finally, numerical tests onsome real-life problems, such as a Van der Waals equation of state and the conversion problem from the chemicalengineering, among others are presented, which confirm the theoretical results to great extent of this study.
Petko D Proinov - One of the best experts on this subject based on the ideXlab platform.
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general local convergence theory for a class of iterative processes and its applications to newton s method
Journal of Complexity, 2009Co-Authors: Petko D ProinovAbstract:General local convergence theorems with order of convergence r>=1 are provided for iterative processes of the type x"n"+"1=Tx"n, where T:D@?X->X is an Iteration Function in a metric space X. The new local convergence theory is applied to Newton Iteration for simple zeros of nonlinear operators in Banach spaces as well as to Schroder Iteration for multiple zeros of polynomials and analytic Functions. The theory is also applied to establish a general theorem for the uniqueness ball of nonlinear equations in Banach spaces. The new results extend and improve some results of [K. Docev, Uber Newtonsche Iterationen, C. R. Acad. Bulg. Sci. 36 (1962) 695-701; J.F. Traub, H. Wozniakowski, Convergence and complexity of Newton Iteration for operator equations, J. Assoc. Comput. Mach. 26 (1979) 250-258; S. Smale, Newton's method estimates from data at one point, in: R.E. Ewing, K.E. Gross, C.F. Martin (Eds.), The Merging of Disciplines: New Direction in Pure, Applied, and Computational Mathematics, Springer, New York, 1986, pp. 185-196; P. Tilli, Convergence conditions of some methods for the simultaneous computation of polynomial zeros, Calcolo 35 (1998) 3-15; X.H. Wang, Convergence of Newton's method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000) 123-134; I.K. Argyros, J.M. Gutierrez, A unified approach for enlarging the radius of convergence for Newton's method and applications, Nonlinear Funct. Anal. Appl. 10 (2005) 555-563; M. Giusti, G. Lecerf, B. Salvy, J.-C. Yakoubsohn, Location and approximation of clusters of zeros of analytic Functions, Found. Comput. Math. 5 (3) (2005) 257-311], and others.
Miquel Grau - One of the best experts on this subject based on the ideXlab platform.
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an improvement of the euler chebyshev iterative method
Journal of Mathematical Analysis and Applications, 2006Co-Authors: Miquel Grau, Jose Luis DiazbarreroAbstract:Abstract We present a new method for the computation of the solutions of nonlinear equations when it is necessary to use high precision. We improve the Euler–Chebyshev iterative method which is a generalization of an improvement of Newton's method. A symbolic computation allows us to find the best coefficients respect to the local order of convergence. The adaptation of the strategy presented here gives an additional Iteration Function with an additional evaluation of the Function. It provides a lower cost if we use adaptive multi-precision arithmetics. The numerical results computed using this system, with a floating point representing a maximum of 210 decimal digits, support this theory.
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Iterative method generated by inverse interpolation with additional evaluations
Numerical Algorithms, 2005Co-Authors: Miquel Grau, Josep M. PerisAbstract:An improvement of the iterative methods based on one point Iteration Function, with or without memory, using n points with the same amount of information in each point and generated by the inverse polynomial interpolation is given. The adaptation of the strategy presented here gives a new Iteration Function with a new evaluation of the Function which increases the local order of convergence dramatically. This method is generalized to r evaluations of the Function. This method for the computation of solutions of nonlinear equations is interesting when it is necessary to get high precision because it provides a lower cost when we use adaptive multi-precision arithmetics.
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An Improvement to the Computing of Nonlinear Equation Solutions
Numerical Algorithms, 2003Co-Authors: Miquel GrauAbstract:In this paper, we suggest an improvement to the iterative methods based on the inverse interpolation polynomial, also referred to as the generalized Hermite interpolation, which increases the local order of convergence. A symbolic computation allows us to find the best coefficients with regard to the order of convergence. The adaptation of the strategy presented here gives a new Iteration Function with a new evaluation of the Function. It also shows a smaller cost if we use adaptive multi-precision arithmetic. The numerical results computed using this system, with a floating point system representing 200 and 1000 decimal digits support this theory.
Jie Wang - One of the best experts on this subject based on the ideXlab platform.
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the Iteration Function on netpad
International Conference on Computer Science and Education, 2019Co-Authors: Jie Wang, Yongsheng Rao, Ruxian Chen, Hao Guan, Ying Wang, Xiaohong ShiAbstract:Iteration is a special graphic transformation similar to the recursive algorithm in programs, which can effectively solve some specific mathematical problems. At present, most dynamic geometry systems(DGS) have the Iteration Function, which meets the demand of teaching. NetPad, one of the DGSs, has optimized the Iteration Function on the basis of other sketchpads. This paper introduces the Iteration Function of NetPad. It provides the implicit Iteration, random color hierarchy of each Iteration object, trajectory Iteration and Iteration of Iteration. Through teaching cases, the superiority of NetPad in Iteration Function is verified.
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ICCSE - The Iteration Function on NetPad
2019 14th International Conference on Computer Science & Education (ICCSE), 2019Co-Authors: Jie Wang, Yongsheng Rao, Ruxian Chen, Hao Guan, Ying Wang, Xiaohong ShiAbstract:Iteration is a special graphic transformation similar to the recursive algorithm in programs, which can effectively solve some specific mathematical problems. At present, most dynamic geometry systems(DGS) have the Iteration Function, which meets the demand of teaching. NetPad, one of the DGSs, has optimized the Iteration Function on the basis of other sketchpads. This paper introduces the Iteration Function of NetPad. It provides the implicit Iteration, random color hierarchy of each Iteration object, trajectory Iteration and Iteration of Iteration. Through teaching cases, the superiority of NetPad in Iteration Function is verified.
