TY - JOUR
AU - Cătinaş, Emil
AU - Păvăloiu, I
PY - 1998/02/01
Y2 - 2024/05/24
TI - On some interpolatory iterative methods for the second degree polynomial operators (I)
JF - Rev. Anal. Numér. Théor. Approx.
JA - Rev. Anal. Numér. Théor. Approx.
VL - 27
IS - 1
SE - Articles
DO -
UR - https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art5
SP - 33-45
AB - <p>In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree 2 on Banach spaces, \(F:X\rightarrow Y\).</p><p>The convergence conditions in this case are simplified, as the divided difference of order 3 is the null trilinear operator.</p><p>As particular cases, we study the eigenproblem for quadratic matrices and integral equations of Volterra type.</p><p>We obtain semilocal convergence results, which show the r-convergence orders of the iterates.</p>
ER -