Journal of applied mathematics & informatics

  • 제6권2호
  • /
  • Pages.393-406
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  • 1999
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  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

AFFINE INVARIANT LOCAL CONVERGENCE THEOREMS FOR INEXACT NEWTON-LIKE METHODS

  • 발행 : 1999.06.01

⟨ 이전 논문 다음 논문 ⟩

초록

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

키워드

참고문헌

  1. J. Comput. Appl. Math. v.36 On the convergence of some projection methods with perturbation Argyros,I.K
  2. Southwest Journal of Pure App. Math. v.1 Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method Argyros,I.K
  3. Relations between forcing sequences and inexact Newton iterates on Banach space Argyros,I.K
  4. The Theory and Application of Iteration Methods Argyros,I.K;Szidarovszky,F
  5. SIAM J. Numer. Anal. v.24 no.2 A local convergence theory for combined inexact Newton/finite difference projection methods Brown,P.N
  6. SIAM J. Numer. Anal. v.19 no.2 Inexat Newton methods Dembo,R.S.;Eisenstat,S.C;Steihaug,T.
  7. J. Comput. Appl. Math. v.79 A new semilocal convergence theorem for Newton's method Gutierrez,J.M
  8. G.P.Functional Analysis Kantorovich,L.V;Akilov
  9. SIAM J. Optimiz. Th. Appl. v.63 no.3 On Qorder and Rorder of convergence Potra,F.A
  10. SIAM J. Numer Anal. v.21 no.3 Local convergence of inexact Newton methods Ypma,T.J.