Solving equations by Hermite type inverse interpolation

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.

Crăciun Iancu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

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

Hermite interpolation; inverse interpolation; nonlinear equations in R; iterative methods; multistep method; convergence order

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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).

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