메뉴 건너뛰기




Volumn 26, Issue 3, 2005, Pages 385-405

On convergence domains of newton's and modified newton methods

Author keywords

smoothness; Modified Newton method; Newton method; Operator equations; Regular smoothness

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FUNCTIONS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS;

EID: 23744468230     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1081/NFA-200067300     Document Type: Article
Times cited : (14)

References (12)
  • 1
    • 0347603934 scopus 로고    scopus 로고
    • Newton-Kantorovich approximations when the derivative is Hölderian: Old and new results
    • F. Cianciaruso and E. De Pascale (2003). Newton-Kantorovich approximations when the derivative is Hölderian: Old and new results. Numer. Func. Anal. Optim. 24:713-723.
    • (2003) Numer. Func. Anal. Optim. , vol.24 , pp. 713-723
    • Cianciaruso, F.1    De Pascale, E.2
  • 2
    • 0346751436 scopus 로고
    • Some remarks on the Newton-Kantorovich method for nonlinear equations with Holder continuous linearizations
    • [Russian]
    • N. T. Demidovich, P. P. Zabreiko, and Ju. V. Lysenko (1993). Some remarks on the Newton-Kantorovich method for nonlinear equations with Holder continuous linearizations [Russian]. Izv. Akad. Nauk Belaruss 3:22-26.
    • (1993) Izv. Akad. Nauk Belaruss , vol.3 , pp. 22-26
    • Demidovich, N.T.1    Zabreiko, P.P.2    Lysenko, J.V.3
  • 3
    • 0040389742 scopus 로고
    • Newton's method under a weak smoothness assumption
    • A. Galperin and Z. Waksman (1991). Newton's method under a weak smoothness assumption. J. Comput. Appl. Math. 35:207-215.
    • (1991) J. Comput. Appl. Math. , vol.35 , pp. 207-215
    • Galperin, A.1    Waksman, Z.2
  • 4
  • 5
    • 1842834754 scopus 로고    scopus 로고
    • Newton-type methods under regular smoothness
    • A. Galperin and Z. Waksman (1996). Newton-type methods under regular smoothness. Numer. Func. Anal. Optim. 17:259-291.
    • (1996) Numer. Func. Anal. Optim. , vol.17 , pp. 259-291
    • Galperin, A.1    Waksman, Z.2
  • 6
    • 0346343079 scopus 로고    scopus 로고
    • Kantorovich's majorization and functional equations
    • A. Galperin (2003). Kantorovich's majorization and functional equations. Numer. Func. Anal. Optim. 24:783-811.
    • (2003) Numer. Func. Anal. Optim. , vol.24 , pp. 783-811
    • Galperin, A.1
  • 7
    • 0343250848 scopus 로고    scopus 로고
    • The convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement
    • E. De Pascale and P. P. Zabreiko (1998). The convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement. Z. Anal. Anwend. 17:271-280.
    • (1998) Z. Anal. Anwend. , vol.17 , pp. 271-280
    • De Pascale, E.1    Zabreiko, P.P.2
  • 8
    • 0006833092 scopus 로고
    • Conditions for convergence of the Newton-Kantorovich method for nonlinear equations with Hölder linearizations
    • [Russian]
    • Ju. V. Lysenko (1994). Conditions for convergence of the Newton-Kantorovich method for nonlinear equations with Hölder linearizations [Russian]. Dokl. Akad. Nauk BSSR 38:20-24.
    • (1994) Dokl. Akad. Nauk BSSR , vol.38 , pp. 20-24
    • Lysenko, J.V.1
  • 9
    • 0004267646 scopus 로고
    • Princeton, NJ: Princeton University Press
    • R. T. Rockafellar (1967). Convex Analysis. Princeton, NJ: Princeton University Press.
    • (1967) Convex Analysis
    • Rockafellar, R.T.1
  • 10
    • 0006838912 scopus 로고
    • On conditions for the applicability of Newton's method
    • [Russian]
    • B. A. Vertgeim (1956). On conditions for the applicability of Newton's method [Russian]. Dokl. Akad. Nauk SSSR 110:719-722.
    • (1956) Dokl. Akad. Nauk SSSR , vol.110 , pp. 719-722
    • Vertgeim, B.A.1
  • 11
    • 0346751430 scopus 로고
    • On some methods of the approximate solution of nonlinear functional equations in Banach spaces
    • [Russian]
    • B. A. Vertgeim (1957). On some methods of the approximate solution of nonlinear functional equations in Banach spaces [Russian]. Uspekhi Mat. Nauk 12:160-169.
    • (1957) Uspekhi Mat. Nauk , vol.12 , pp. 160-169
    • Vertgeim, B.A.1
  • 12
    • 18444367807 scopus 로고
    • Engl. Transi.
    • [1960 Engl. Transi.: Am. Math. Soc. Transi. 16(2):378-382.]
    • (1960) Am. Math. Soc. Transi. , vol.16 , Issue.2 , pp. 378-382


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.