Abstract
Let \(X_{1},X_{2}\) be two Banach spaces and \(f:X_{1}\rightarrow X_{2}\) a nonlinear equation. We study the chord method for solving the equation \(f\left( x\right) =0\). Assuming the first order divided differences of \(f\) satisfy a Holder type condition, we obtain sufficient convergence conditions and error estimations at each step.
Authors
Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)
Keywords
chord method; divided differences; Holder condition
Cite this paper as:
I. Păvăloiu, Remarks on the secant method for the solution of nonlinear operatorial equations, Research Seminars, Seminar on Mathematical Analysis, Preprint no. 7 (1991), pp. 127-132.
About this paper
Journal
Seminar on mathematical analysis,
Preprint
Publisher Name
“Babes-Bolyai” University,
Faculty of Mathematics,
Research Seminars
DOI
Not available yet.
References
[1] Argyros, I.K., The secant method and fixed points of nonlinear operators, Mh. Math. 106, 85 94 (1988).
[2] Dennis, J.E., Toward a unified convergence theory for Newton like methods, Nonlinear Functional analysis and Applications (Ed. by L.B. Rall), pp. 425–472, New York, John Wiley (1986).
[3] Pavaloiu, I., Introduction to the Theory of Approximation of Equations Solutions, Dacia Ed., Cluj-Napoca, 1976 (in Romanian)