Geodesic
On a secant-like method for solving generalized equations
Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 313-320

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In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.
In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances involved and a larger radius of convergence are obtained.
DOI : 10.21136/MB.2008.140620
Classification : 47J25, 49M15, 65G99, 65J15, 65K10
Keywords: secant-like method; generalized equations; Aubin continuity; radius of convergence; divided difference 
Argyros, Ioannis K.; Hilout, Said. On a secant-like method for solving generalized equations. Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 313-320. doi: 10.21136/MB.2008.140620
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