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A semilocal convergence analysis is provided for Newton's method in a
Banach space. The inverses of the operators involved are only locally HÖlderian. We make use of a point-based approximation and center-HÖlderian hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.
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참고문헌 (6)
참고문헌 신청
Argyros, I.K / 2000 / Advances in the E±ciency of Computational Methods and Applications / World Scienti?c Publ. Co
Argyros, I.K / 2003 / An improved error analysis for Newton-like methods under generalized condi-tions / J. Comput. Appl. Math 157 (1) : 169 ~ 185
Ioannis K. Argyros / 2008 / ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS / 순수 및 응용수학 15 (2) : 111 ~ 120
Kantorovich, L.V / 1982 / Functional Analysis in Normed Spaces / Pergamon Press
Robinson, S.M / 1991 / An implicit function theorem for a class of nonsmooth functions / Mathematics of Operations Research 16 (2) : 292 ~ 309
Argyros, I.K / 2003 / An improved error analysis for Newton-like methods under generalized condi-tions / J. Comput. Appl. Math 157 (1) : 169 ~ 185
Ioannis K. Argyros / 2008 / ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS / 순수 및 응용수학 15 (2) : 111 ~ 120
Kantorovich, L.V / 1982 / Functional Analysis in Normed Spaces / Pergamon Press
Robinson, S.M / 1991 / An implicit function theorem for a class of nonsmooth functions / Mathematics of Operations Research 16 (2) : 292 ~ 309
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