Error estimation in numerical solution of equations and systems of equations

Authors

  • Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Abstract views: 213

Abstract

In [7], [8], M. Urabe studies the numerical convergence and error estimation in the case of operatorial equation solution by means of iteration methods. Urabe's results refer to operatorial equations in complete metric spaces, while as application the numerical convergence of Newton's method in Banach spaces is studied. Using Urabe's results, M. Fujii [1] studies the same problems for Steffensen's method and the chord method applied to equations with real functions. In [6], Urabe's method is applied to a large class of iteration methods with arbitrary convergence order. We propose further down to extend Urabe's results to the case of the Gauss-Seidel method for systems of equations in metric spaces.

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References

Fujii, M., Remarks to Accelerated Iterative Processes for Numerical Solution of Equations, J. Sci. Hiroshima Univ. Ser. A-I, 27 (1963), 97-118, https://doi.org/10.32917/hmj/1206139554

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Păvăloiu, I., Estimation des erreurs dans la résolution numérique des systèmes d'équations dans des espaces métriques. Seminar of Functional Analysis and Numerical Methods. Preprint Nr.1, (1987), 121-129.

Păvăloiu, I., Délimitations des erreurs dans la résolution numérique des systèmes d'équations. Research Seminars. Seminar on Mathematical analysis. Preprint Nr.7, (1988), 167-178.

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Urabe, M., Convergence of numerical iteration in solution of equations. J. Sci. Hirooshima, Univ.Ser. A, 19 (1956), 479-489, https://doi.org/10.32917/hmj/1556071264

Urabe, M., Error Estimation in Numerical Solution of Equations by Iteration Processes, J. Sci. Hiroshima Univ. Ser. A-I, 26, (1962), 77-91, https://doi.org/10.32917/hmj/1206139729

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Published

1992-08-01

How to Cite

Păvăloiu, I. (1992). Error estimation in numerical solution of equations and systems of equations. Rev. Anal. Numér. Théor. Approx., 21(2), 153–165. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1992-vol21-no2-art8

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