On some interpolatory iterative methods for the second degree polynomial operators (I)

Emil Cătinaş; I Păvăloiu

Authors

Emil Cătinaş Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
I Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

Abstract views: 277

Abstract

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.

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