Relevant bibliographies by topics / Iterative methods (Mathematics)

Academic literature on the topic 'Iterative methods (Mathematics)'

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Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Iterative methods (Mathematics)"

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Rafiq, Arif, Sifat Hussain, Farooq Ahmad, and Muhammad Awais. "New iterative methods." Applied Mathematics and Computation 189, no. 2 (June 2007): 1260–67. http://dx.doi.org/10.1016/j.amc.2006.12.042.

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Beauwens, Robert. "Iterative solution methods." Applied Numerical Mathematics 51, no. 4 (December 2004): 437–50. http://dx.doi.org/10.1016/j.apnum.2004.06.003.

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Lin, R. F., H. M. Ren, Z. Šmarda, Q. B. Wu, Y. Khan, and J. L. Hu. "New Families of Third-Order Iterative Methods for Finding Multiple Roots." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/812072.

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Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). The presented families include many third-order methods for finding multiple roots, such as the known Dong's methods and Neta's method. Some new concrete iterative methods are provided. Each member of the two families requires two evaluations of the function and one of its first derivative per iteration. All these methods require the knowledge of the multiplicity. The obtained methods are also compared in their performance with various other iteration methods via numerical examples, and it is observed that these have better performance than the modified Newton method, and demonstrate at least equal performance to iterative methods of the same order.
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Geiser, Jürgen. "Computing Exponential for Iterative Splitting Methods: Algorithms and Applications." Journal of Applied Mathematics 2011 (2011): 1–27. http://dx.doi.org/10.1155/2011/193781.

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Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration and recovering of higher-order schemes can be achieved. From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In this paper, we concentrate on developing fast algorithms to solve the iterative splitting scheme. First, we reformulate the iterative splitting scheme into an integral notation of matrix exponential. In this notation, we consider fast approximation schemes to the integral formulations, also known as -functions. Second, the error analysis is explained and applied to the integral formulations. The novelty is to compute cheaply the decoupled exp-matrices and apply only cheap matrix-vector multiplications for the higher-order terms. In general, we discuss an elegant way of embedding recently survey on methods for computing matrix exponential with respect to iterative splitting schemes. We present numerical benchmark examples, that compared standard splitting schemes with the higher-order iterative schemes. A real-life application in contaminant transport as a two phase model is discussed and the fast computations of the operator splitting method is explained.
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Khattri, S. K., and R. P. Agarwal. "Derivative-Free Optimal Iterative Methods." Computational Methods in Applied Mathematics 10, no. 4 (2010): 368–75. http://dx.doi.org/10.2478/cmam-2010-0022.

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AbstractIn this study, we develop an optimal family of derivative-free iterative methods. Convergence analysis shows that the methods are fourth order convergent, which is also verified numerically. The methods require three functional evaluations during each iteration. Though the methods are independent of derivatives, computa- tional results demonstrate that the family of methods are efficient and demonstrate equal or better performance as compared with many well-known methods and the clas- sical Newton method. Through optimization we derive an optimal value for the free parameter and implement it adaptively, which enhances the convergence order without increasing functional evaluations.
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Proinov, Petko D., and Maria T. Vasileva. "A New Family of High-Order Ehrlich-Type Iterative Methods." Mathematics 9, no. 16 (August 5, 2021): 1855. http://dx.doi.org/10.3390/math9161855.

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One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.
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Vabishchevich, Petr N. "Iterative Methods for Solving Convection-diffusion Problem." Computational Methods in Applied Mathematics 2, no. 4 (2002): 410–44. http://dx.doi.org/10.2478/cmam-2002-0023.

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AbstractTo obtain an approximate solution of the steady-state convectiondiffusion problem, it is necessary to solve the corresponding system of linear algebraic equations. The basic peculiarity of these LA systems is connected with the fact that they have non-symmetric matrices. We discuss the questions of approximate solution of 2D convection-diffusion problems on the basis of two- and three-level iterative methods. The general theory of iterative methods of solving grid equations is used to present the material of the paper. The basic problems of constructing grid approximations for steady-state convection-diffusion problems are considered. We start with the consideration of the Dirichlet problem for the differential equation with a convective term in the divergent, nondivergent, and skew-symmetric forms. Next, the corresponding grid problems are constructed. And, finally, iterative methods are used to solve approximately the above grid problems. Primary consideration is given to the study of the dependence of the number of iteration on the Peclet number, which is the ratio of the convective transport to the diffusive one.
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Bai, Zhong-Zhi. "Regularized HSS iteration methods for stabilized saddle-point problems." IMA Journal of Numerical Analysis 39, no. 4 (July 31, 2018): 1888–923. http://dx.doi.org/10.1093/imanum/dry046.

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Abstract We extend the regularized Hermitian and skew-Hermitian splitting (RHSS) iteration methods for standard saddle-point problems to stabilized saddle-point problems and establish the corresponding unconditional convergence theory for the resulting methods. Besides being used as stationary iterative solvers, this class of RHSS methods can also be used as preconditioners for Krylov subspace methods. It is shown that the eigenvalues of the corresponding preconditioned matrix are clustered at a small number of points in the interval $(0, \, 2)$ when the iteration parameter is close to $0$ and, furthermore, they can be clustered near $0$ and $2$ when the regularization matrix is appropriately chosen. Numerical results on stabilized saddle-point problems arising from finite element discretizations of an optimal boundary control problem and of a Cahn–Hilliard image inpainting problem, as well as from the Gauss–Newton linearization of a nonlinear image restoration problem, show that the RHSS iteration method significantly outperforms the Hermitian and skew-Hermitian splitting iteration method in iteration counts and computing times when they are used either as linear iterative solvers or as matrix splitting preconditioners for Krylov subspace methods, and optimal convergence behavior can be achieved when using inexact variants of the proposed RHSS preconditioners.
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Javidi, M. "Iterative methods to nonlinear equations." Applied Mathematics and Computation 193, no. 2 (November 2007): 360–65. http://dx.doi.org/10.1016/j.amc.2007.03.068.

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Huhtanen, Marko, and Olavi Nevanlinna. "Minimal decompositions and iterative methods." Numerische Mathematik 86, no. 2 (August 2000): 257–81. http://dx.doi.org/10.1007/pl00005406.

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Dissertations / Theses on the topic "Iterative methods (Mathematics)"

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McKay, Melanie. "Iterative methods for incompressible flow." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28063.

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The goal of this thesis is to illustrate the effectiveness of iterative methods on the discretized Navier Stokes equations. The standard lid-driven cavity in both 2-D and 3-D test cases are examined and compared with published results of the same type. The numerical results are obtained by reducing the partial differential equations (PDEs) to a system of algebraic equations with a stabilized P1-P1 Finite Element Method (FEM) in space. Gear's Backward Difference Formula (BDF2) and an adaptive time stepping scheme utilizing a first order Backward Euler (BE) startup and BDF2 are then utilized to discretizc the time derivative of the Javier-Stokes equations. The iterative method used is the Generalized Minimal Residual (GMRES) along with the selected preconditioners Incomplete LU Factorization (ILU), Jacobi preconditioner and the Block Jacobi preconditioner.
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Kwan, Chun-kit, and 關進傑. "Fast iterative methods for image restoration." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31224520.

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Karelius, Fanny. "Stationary iterative methods : Five methods and illustrative examples." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-69711.

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Systems of large sparse linear equations frequently arise in engineering and science. Therefore, there is a great need for methods that can solve these systems. In this thesis we will present three of the earliest and simplest iterative methods and also look at two more sophisticated methods. We will study their rate of convergence and illustrate them with examples.
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Kwan, Chun-kit. "Fast iterative methods for image restoration /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk:8888/cgi-bin/hkuto%5Ftoc%5Fpdf?B22956281.

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Ho, Ching-wah. "Iterative methods for the Robbins problem /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22054789.

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何正華 and Ching-wah Ho. "Iterative methods for the Robbins problem." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31222572.

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Sivaloganathan, S. "Iterative methods for large sparse systems of equations." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370302.

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Roberts, Harriet. "Preconditioned iterative methods on virtual shared memory machines." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-07292009-090522/.

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須成忠 and Cheng-zhong Xu. "Iterative methods for dynamic load balancing in multicomputers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233302.

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Xu, Cheng-zhong. "Iterative methods for dynamic load balancing in multicomputers /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13458905.

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Books on the topic "Iterative methods (Mathematics)"

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Axelsson, O. Iterative solution methods. Cambridge [England]: Cambridge University Press, 1994.

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Byrne, C. L. Applied iterative methods. Wellesley, Mass: AK Peters, 2008.

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Ilʹin, V. P. Iterative incomplete factorization methods. Singapore: World Scientific, 1992.

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1951-, Ésik Zoltán, ed. Iteration theories: The equational logic of iterative processes. Berlin: Springer-Verlag, 1993.

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Argyos, Ioannis. Advances on iterative procedures. New York: Nova Science Publishers, 2011.

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Varga, Richard S. Matrix Iterative Analysis. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2009.

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Kelley, C. T. Iterative methods for linear and nonlinear equations. Philadelphia: Society for Industrial and Applied Mathematics, 1995.

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Weiss, Rüdiger. Parameter-free iterative linear solvers. Berlin: Akademie Verlag, 1996.

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1958-, Chan Raymond H., Chan Tony F, and Golub Gene H. 1932-, eds. Iterative methods in scientific computing. Singapore: Springer, 1997.

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Bloom, Stephen L. Iteration Theories: The Equational Logic of Iterative Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993.

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Book chapters on the topic "Iterative methods (Mathematics)"

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Björck, Åke. "Iterative Methods." In Texts in Applied Mathematics, 613–781. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05089-8_4.

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Van de Velde, Eric F. "Iterative Methods." In Texts in Applied Mathematics, 67–96. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0849-5_3.

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Lyche, Tom, and Jean-Louis Merrien. "Iterative Methods." In Exercises in Computational Mathematics with MATLAB, 65–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43511-3_5.

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Bartels, Sören. "Iterative Solution Methods." In Texts in Applied Mathematics, 209–44. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32354-1_5.

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Leblond, Michel, François Rousselle, and Christophe Renaud. "Generalized Block Iterative Methods." In Mathematics and Visualization, 261–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05105-4_14.

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Axelsson, Owe. "Classical Iterative Methods." In Encyclopedia of Applied and Computational Mathematics, 205–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_242.

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Bird, John. "Solving equations by iterative methods." In Engineering Mathematics, 154–57. 8th edition. | Abingdon, Oxon ; New York, NY : Routledge, 2017.: Routledge, 2017. http://dx.doi.org/10.4324/9781315561851-21.

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Petković, Miodrag. "Iterative methods without derivatives." In Lecture Notes in Mathematics, 31–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0083602.

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Cegielski, Andrzej. "Convergence of Iterative Methods." In Lecture Notes in Mathematics, 105–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30901-4_3.

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Toselli, Andrea, and Olof B. Widlund. "Primal Iterative Substructuring Methods." In Springer Series in Computational Mathematics, 113–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26662-3_5.

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Conference papers on the topic "Iterative methods (Mathematics)"

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Geiser, Jürgen, José L. Hueso, and Eulalia Martínez. "Parallel iterative splitting methods: Algorithms and applications." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026671.

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Chicharro, F. I., A. Cordero, and J. R. Torregrosa. "Stability of different families of iterative methods with memory." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043939.

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Diene, Oumar, Amit Bhaya, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Study of the Robustness of Iterative Methods for Linear Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241491.

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Geiser, Jürgen, and Dennis Ogiermann. "Adaptive-iterative implicit methods for solving hodgkin-huxley type systems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081365.

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Amat, Sergio, Sonia Busquier, Miguel Ángel Hernández-Verón, Ángel Alberto Magreñán, and Lara Orcos. "Comparing of the behaviour of iterative methods based on different means." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027175.

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Geiser, Jürgen, and Karsten Bartecki. "Additive, multiplicative and iterative splitting methods for Maxwell equations: Algorithms and applications." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044072.

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Muthuvalu, Mohana Sundaram, Elayaraja Aruchunan, Majid Khan Majahar Ali, and Jumat Sulaiman. "Preconditioned Jacobi-type iterative methods for solving Fredholm integral equations of the second kind." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954529.

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Koleva, M. N., Michail D. Todorov, and Christo I. Christov. "Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 3rd International Conference—AMiTaNS'11. AIP, 2011. http://dx.doi.org/10.1063/1.3659948.

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Nedzhibov, Gyurhan H., George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "An approach to accelerate iterative methods for solving nonlinear operator equations." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '11): Proceedings of the 37th International Conference. AIP, 2011. http://dx.doi.org/10.1063/1.3664358.

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Amat, S., S. Busquier, and Á. A. Magreñán. "On a Newton-type family of high-order iterative methods for some matrix functions." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043941.

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