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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 289 - 293 (5page)
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We recently showed in [5] a semilocal convergence theorem that guarantees convergence of Newton’s method to a locally unique solution of a nonlinear equation under hypotheses weaker than those of the Newton–Kantorovich theorem [7]. Here, we first weaken Miranda’s theorem [1], [9], [10], which is a generalization of the intermediate value theorem. Then, we show that operators satisfying the weakened Newton–Kantorovich conditions satisfy those of the weakened Miranda’s theorem.
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참고문헌 (10)
참고문헌 신청
C. Miranda / 1940 / Un osservatione su un teorema di Brower / Boll. Unione Math. Ital. Ser. II 3 : 5 ~ 7
G. Alefeld / 2001 / On the existence theorems of Kantorovich, Moore and Miranda, Topics in Numerical Analysis / Springer : 21 ~ 28
I.K. Argyros / / On a class of Newton?like methods for solving nonlinear analysis / J. Comput. Appl. Math
I.K. Argyros / 1993 / The theory and applications of iteration methods / C.R.C. Press Inc.
I.K. Argyros / 2004 / On the Newton?Kantorovich hypothesis for solving equations / J. Comput. Appl. Math 169 : 315 ~ 332
G. Alefeld / 2001 / On the existence theorems of Kantorovich, Moore and Miranda, Topics in Numerical Analysis / Springer : 21 ~ 28
I.K. Argyros / / On a class of Newton?like methods for solving nonlinear analysis / J. Comput. Appl. Math
I.K. Argyros / 1993 / The theory and applications of iteration methods / C.R.C. Press Inc.
I.K. Argyros / 2004 / On the Newton?Kantorovich hypothesis for solving equations / J. Comput. Appl. Math 169 : 315 ~ 332
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