Abstract
We study the convergence of an iterative method for solving the equation (fleft( xright) =0, f:Isubseteq mathbb{Rrightarrow R}). The iterative method is obtained by the Hermite inverse interpolation polynomial. We show that the convergence order of this method is given by the unique positive solution of a polynomial equation with coefficients given by the multiplicity orders. We consider the particular instance of two interpolation nodes and we determine the resulted methods.
Authors
Crăciun Iancu, Ion Păvăloiu
Title
Original title (in French)
La resolution des équations par interpolation inverse de type Hermite
English translation of the title
Solving equations by Hermite inverse interpolation
Keywords
Hermite interpolation; inverse interpolation; nonlinear equations in R; iterative methods; multistep method; convergence order
References
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[4] I. Pavaloiu, Rezolvarea ecua¸iilor prin interpolare, Ed. Dacia, 1981.
[5] I. Pavaloiu, Introducere in aproximarea solutiilor ecuatiilor, Ed. Dacia, 1976.
[6] D.D. Stancu, Asupra formulei de interpolare a lui Hermite si a unor aplicatii ale acesteia, Studii ¸si Cercet. Mat. (Cluj), 3-4 VIII, (1957), 339-355.
[7] J.F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall Series in Automatic Computation 1964.
[8] B.A. Turowicz, Sur les derivees d’ordre superiour d’une fonction inverse, Colloq. Math., (1959), 83–87.
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About this paper
Cite this paper as:
C. Iancu, I. Păvăloiu, La resolution des équations par interpolation inverse de type Hermite, Mathematica (Cluj), 26(49) (1984) no. 2, pp. 115-123 (in French).
Journal
Mathematica
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