Atsumasa Kondo · Mathematische Annalen · 2024
We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.
Cited by 1Open access
Snehashish Chakraverty, Rajarama Mohan Jena, Subrat Kumar Jena · 2022
Variational iterative method (VIM) is again a semi-analytical technique like homotopy perturbation method (HPM) and Adomian decomposition method (ADM) for solving both linear and nonlinear ordinary/partial/fractional differential equations. This technique is based on the application of restricted variations and correction functional. VIM does not require small parameters in the differential equation and generates a solution as a sequence of iterations. It does not need the nonlinearities to be differentiable with respect to the dependent variable and its derivatives. This chapter first discusses the fundamental concept of VIM. Further, this method is used to deal with two problems: a linear one-dimensional fractional heat-like equation and a nonlinear fractional advection equation. The test problems used in this chapter indicate that VIM is an effective way to solve linear/nonlinear fractional differential equations. The series generally converges with an increase in terms, but the compact solution form may not always be expected.
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2008
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Riccardo Fazio · International Journal of Non-Linear Mechanics · 2019
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Philippe Rigaux · 2004
Given a large set of items and a set of users, we consider the problem of collecting user preferences - or ratings - on items. The paper describes a simple method which provides an approximate solution to the problem without requiring each user to rate each item. The method relies on an iterative process. Each step, or ballot, requires each user to rate a sample of the items. A collaborative filtering algorithm is then performed to predict the missing ratings as well as their level of confidence (which is initially 0). Perfoming a new ballot allows to improve the accuracy of predictions. The administrator of the system is responsible for stopping the iteration when a satisfactory level is reached.We apply this method to the assignment of reviewers to papers prior to the review phase of conference management, and describe its implementation in the MYREVIEW web-based system.
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Geiser, Jürgen · edoc Publication server (Humboldt University of Berlin) · 2011
In this paper we describe an iterative operator-splitting method for bounded operators. The contribution is a novel iterative method, that can be applied as a splitting method for ordinary and partial differential equations. A simple relation between the number of iterative steps and the order of the splitting scheme, can made it as an alternative method to consider it as a time decomposition method. The iterative splitting scheme is interested on physical problem, while the original problem is not divided as in standard splitting schemes. We present error bounds for the iterative splitting methods in the presence of bounded operators. We discuss efficient algorithms to compute the integral formulation of the splitting scheme. In experiments, we consider the benefits of the novel splitting method with respect to their number of iterations and time steps. Ordinary differential equations and convection-diffusion-reaction equations are presented in the numerical results.
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Aydin, Zafer, Yucel Altunbasak, Borodovsky, Mark · Figshare · 2011
<b>Copyright information:</b>Taken from "Protein secondary structure prediction for a single-sequence using hidden semi-Markov models"BMC Bioinformatics 2006;7():178-178.Published online 30 Mar 2006PMCID:PMC1479840. Initial set of model parameters is precomputed from the general training set.
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Aydin, Zafer, Yucel Altunbasak, Borodovsky, Mark · Figshare · 2011
<b>Copyright information:</b>Taken from "Protein secondary structure prediction for a single-sequence using hidden semi-Markov models"BMC Bioinformatics 2006;7():178-178.Published online 30 Mar 2006PMCID:PMC1479840. Initial set of model parameters is precomputed from the general training set.
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David M. Young · Elsevier eBooks · 1971
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A. A. Fonarev · Mathematical Notes · 1981
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Richard Hodges, Y. Rahmat–Samii · 2002
An iterative solution method (POHM iterative) has been developed which is suitable for modelling small, intricate antennas that are mounted on comparatively large bodies. The method provides radiation pattern, impedance, gain and RCS information. A computer program was developed to test the POHM iterative algorithm. Results shows good agreement with moment method calculations and experimental data.
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В. Т. Жуков, О. Б. Феодоритова, Н. М. Новикова · Matematicheskoe modelirovanie · 2018
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Legesse Kebede · The Astrophysical Journal · 1994
The problems of a direct inversion of a response matrix are discussed. unfolding the data is suggested. The method totally eliminates the possible result of a successful application of the technique on data from a source object is given.
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Varsha Daftardar‐Gejji, Manoj Kumar · Current developments in mathematical sciences · 2018
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Wei Xu, Xiaole Yue, Qun He · 2012
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V.S. Manoranjan · WORLD SCIENTIFIC eBooks · 1996
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Taylor, Jordan · Mendeley Data · 2020
We demonstrate the rapid convergence of an iterative approximation that enables the Crank-Nicolson method for solving partial differential equations to be parallelized with arbitrarily small error, so long as the temporal step size is kept sufficiently small compared to the square of the spatial step size. Unlike the original Crank-Nicolson method, our method can handle non-linear terms. We apply the new method specifically to linear and non-linear 1-D Schrödinger equations, but it can be applied to any parabolic partial differential equation, such as those used to describe heat flow, diffusion, or dynamics of financial markets. The extension of the method to handle cyclic boundary conditions or 3-D wavefunctions is straightforward. Example code is given in C++. Included is the [iterative_parallel_CN.cpp] code file, which can be compiled with $ g++ -fopenmp iterative_parallel_CN.cpp -std=c++11 -lm -Wall -O3 -o iterative_parallel_CN.exe The input file [iterative_parallel_CN.inp] contains the variables to be given to the program when run: $ ./iterative_parallel_CN.exe The results are written to multiple raw files [iterative_parallel_CN_Xiterations_XXXXXX.dat], and one summary file [iterative_parallel_CN_summary.dat]. The raw files can be turned into an animation with gnuplot using the file animate.gpi: $ gnuplot animate.gpi This will produce a GIF of whatever scenario you put into the .inp file (by default, a Gaussian oscillating in a harmonic trap).
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Stephen Devlin, Thomas Treloar, Molly Creagar et al. · Journal of Quantitative Analysis in Sports · 2020
Abstract We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.
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Riccardo Fazio · arXiv (Cornell University) · 2020
The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The definition of a non-iterative transformation method for the celebrated Blasius problem is due to T{ö}pfer and dates more than a century ago. Here we define a non-iterative transformation method for Blasius equation with a moving wall, a slip flow condition or a surface gasification. The defined method allows us to deal with classes of problems in boundary layer theory that, depending on a parameter, admit multiple or no solutions. This approach is particularly convenient when the main interest is on the behaviour of the considered models with respect to the involved parameter. The obtained numerical results are found to be in good agreement with those available in literature.
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Henry C. Thacher · The Computer Journal · 1962
An iterative algorithm is presented for estimating repeated integrals of a function, The estimate is based upon numerical values of the function at a set of arbitrarily-spaced base points, and is equivalent, except for roundoff, to the repeated integral of the interpolating polynomial.
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