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


  • Emil Cătinaş Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
  • I Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania
Abstract views: 243


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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How to Cite

Cătinaş, E., & Păvăloiu, I. (1998). On some interpolatory iterative methods for the second degree polynomial operators (I). Rev. Anal. Numér. Théor. Approx., 27(1), 33–45. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art5