# Remarks on the secant method for the solution of nonlinear operator equations

## 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.

Ion Păvăloiu

## Keywords

chord method; divided differences; Holder condition

## 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)

## PDF

##### 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.

##### Journal

Seminar on mathematical analysis,
Preprint

##### Publisher Name

“Babes-Bolyai” University,
Faculty of Mathematics,
Research Seminars

##### DOI

Not available yet.