Geodesic
Weaker convergence conditions for the secant method
Applications of Mathematics, Tome 59 (2014) no. 3, pp. 265-284

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We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
DOI : 10.1007/s10492-014-0054-6
Classification : 49M15, 65B05, 65G99, 65H10, 65J15, 65N30
Keywords: semilocal convergence; secant method; Banach space; majorizing sequence; Hölder condition; divided difference; Fréchet-derivative 
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Argyros, Ioannis K.; Hilout, Saïd. Weaker convergence conditions for the secant method. Applications of Mathematics, Tome 59 (2014) no. 3, pp. 265-284. doi: 10.1007/s10492-014-0054-6

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