In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree 2 on Banach spaces, \(F:X\rightarrow Y\).

The convergence conditions in this case are simplified, as the divided difference of order 3 is the null trilinear operator.

As particular cases, we study the eigenproblem for quadratic matrices and integral equations of Volterra type.

We obtain semilocal convergence results, which show the r-convergence orders of the iterates.


Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)


chord/secant method; Steffensen method; polynomial operator equation of degree 2 on Banach spaces; divided differences; eigenproblem for quadratic matrices; integral equations of Volterra type; semilocal convergence; r-convergence order.

Cite this paper as:

E. Cătinaş, I. Păvăloiu, On some interpolatory iterative methods for the second degree polynomial operators (I), Rev. Anal. Numér. Théor. Approx., 27 (1998) no. 1, pp. 33-45.


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