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초록· 키워드
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The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.
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참고문헌 (30)
참고문헌 신청
S. Amat / 2008 / A modified Chebyshev’s iterative method with at least sixth order of convergence / Appl. Math. Comput 206(1):164~174
I. K. Argyros / 2008 / Convergence and Application of Newton-type Iterations / Springer
Ioannis Konstantinos Argyros / 2014 / ON THE “TERRA INCOGNITA” FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS / 대한수학회지 51(2):251~266
I. K. Argyros / 2012 / Hilout, Numerical Methods for Equations and its Applications / CRC Press
I. K. Argyros / 2013 / On a new semilocal convergence analysis for the Jarratt method / J. Inequal. Appl 2013(194):16
I. K. Argyros / 2008 / Convergence and Application of Newton-type Iterations / Springer
Ioannis Konstantinos Argyros / 2014 / ON THE “TERRA INCOGNITA” FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS / 대한수학회지 51(2):251~266
I. K. Argyros / 2012 / Hilout, Numerical Methods for Equations and its Applications / CRC Press
I. K. Argyros / 2013 / On a new semilocal convergence analysis for the Jarratt method / J. Inequal. Appl 2013(194):16
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