The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 15 Issue 1
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- Pages.47-55
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- 2008
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
CONCERNING THE RADII OF CONVERGENCE FOR A CERTAIN CLASS OF NEWTON-LIKE METHODS
- Argyros, Ioannis K. (Department of Mathematical Sciences, Cameron University)
- Published : 2008.02.28
Abstract
Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.
Keywords
- Newton-like method;
- modified Newton-like method;
- Banach space;
- local convergence;
- radius of convergence;
- convergence domain