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Volumn 30, Issue 3, 2014, Pages 366-380

A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously

Author keywords

Error estimates; Normed fields; Polynomial zeros; Semilocal convergence; Simultaneous methods; Weierstrass method

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL ANALYSIS;

EID: 84897396535     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2013.11.002     Document Type: Article
Times cited : (22)

References (24)
  • 1
    • 0032163498 scopus 로고    scopus 로고
    • Improvement of a convergence condition for Durand-Kerner iteration
    • P. Batra Improvement of a convergence condition for Durand-Kerner iteration J. Comput. Appl. Math. 96 1998 117 125
    • (1998) J. Comput. Appl. Math. , vol.96 , pp. 117-125
    • Batra, P.1
  • 2
    • 0000999875 scopus 로고
    • Modified Newton method for the simultaneous computation of all roots of a given algebraic equation
    • (in Bulgarian)
    • K. Dochev Modified Newton method for the simultaneous computation of all roots of a given algebraic equation Phys. Math. J. Bulg. Acad. Sci. 5 1962 136 139 (in Bulgarian)
    • (1962) Phys. Math. J. Bulg. Acad. Sci. , vol.5 , pp. 136-139
    • Dochev, K.1
  • 4
    • 33746168220 scopus 로고    scopus 로고
    • The convergence of the Durand-Kerner method for simultaneously finding all zeros of a polynomial
    • D.F. Han The convergence of the Durand-Kerner method for simultaneously finding all zeros of a polynomial J. Comput. Math. 18 2000 567 570
    • (2000) J. Comput. Math. , vol.18 , pp. 567-570
    • Han, D.F.1
  • 5
    • 0000341458 scopus 로고
    • Ein gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
    • I.O. Kerner Ein gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen Numer. Math. 8 1966 290 294
    • (1966) Numer. Math. , vol.8 , pp. 290-294
    • Kerner, I.O.1
  • 6
    • 0039373753 scopus 로고
    • Über Limesbildung und allgemeine Körpertheorie
    • J. Kürschák Über Limesbildung und allgemeine Körpertheorie J. Reine Angew. Math. 142 1913 211 253
    • (1913) J. Reine Angew. Math. , vol.142 , pp. 211-253
    • Kürschák, J.1
  • 8
    • 0030394158 scopus 로고    scopus 로고
    • On initial conditions for the convergence of simultaneous root-finding methods
    • M.S. Petković On initial conditions for the convergence of simultaneous root-finding methods Computing 57 1996 163 177
    • (1996) Computing , vol.57 , pp. 163-177
    • Petković, M.S.1
  • 11
    • 0035501246 scopus 로고    scopus 로고
    • Point estimation of simultaneous methods for solving polynomial equations
    • M.S. Petković, and D. Herceg Point estimation of simultaneous methods for solving polynomial equations J. Comput. Appl. Math. 136 2001 283 307
    • (2001) J. Comput. Appl. Math. , vol.136 , pp. 283-307
    • Petković, M.S.1    Herceg, D.2
  • 12
    • 0032372229 scopus 로고    scopus 로고
    • Safe convergence of simultaneous methods for polynomial zeros
    • M.S. Petković, D. Herceg, and S. Ilić Safe convergence of simultaneous methods for polynomial zeros Numer. Algorithms 17 1998 313 331
    • (1998) Numer. Algorithms , vol.17 , pp. 313-331
    • Petković, M.S.1    Herceg, D.2    Ilić, S.3
  • 13
    • 0042893963 scopus 로고
    • Un procéd é itératif pour la factorisation des polynômes
    • S.B. Prešić Un procéd é itératif pour la factorisation des polynômes C. R. Acad. Sci. Paris Sèr. A 262 1966 862 863
    • (1966) C. R. Acad. Sci. Paris Sèr. A , vol.262 , pp. 862-863
    • Prešić, S.B.1
  • 14
    • 28444458825 scopus 로고
    • A convergence theorem for a method for simultaneous determination of all zeros of a polynomial
    • M.D. Prešić A convergence theorem for a method for simultaneous determination of all zeros of a polynomial Publ. Inst. Math. 28 1980 159 165
    • (1980) Publ. Inst. Math. , vol.28 , pp. 159-165
    • Prešić, M.D.1
  • 15
    • 71649104802 scopus 로고    scopus 로고
    • A new semilocal convergence theorem for the Weierstrass method from data at one point
    • P.D. Proinov A new semilocal convergence theorem for the Weierstrass method from data at one point C. R. Acad. Bulg. Sci. 59 2006 131 136
    • (2006) C. R. Acad. Bulg. Sci. , vol.59 , pp. 131-136
    • Proinov, P.D.1
  • 16
    • 71649104008 scopus 로고    scopus 로고
    • Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros
    • P.D. Proinov Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros C. R. Acad. Bulg. Sci. 59 2006 705 712
    • (2006) C. R. Acad. Bulg. Sci. , vol.59 , pp. 705-712
    • Proinov, P.D.1
  • 17
    • 56949098628 scopus 로고    scopus 로고
    • General local convergence theory for a class of iterative processes and its applications to Newton's method
    • P.D. Proinov General local convergence theory for a class of iterative processes and its applications to Newton's method J. Complexity 25 2009 38 62
    • (2009) J. Complexity , vol.25 , pp. 38-62
    • Proinov, P.D.1
  • 18
    • 71649115541 scopus 로고    scopus 로고
    • New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
    • P.D. Proinov New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems J. Complexity 26 2010 3 42
    • (2010) J. Complexity , vol.26 , pp. 3-42
    • Proinov, P.D.1
  • 20
    • 0000303413 scopus 로고
    • The theory of Smale's point estimation and its applications
    • D. Wang, and F. Zhao The theory of Smale's point estimation and its applications J. Comput. Appl. Math. 60 1995 253 269
    • (1995) J. Comput. Appl. Math. , vol.60 , pp. 253-269
    • Wang, D.1    Zhao, F.2
  • 21
    • 80255130878 scopus 로고
    • Neuer Beweis des satzes, dass jede ganze rationale function einer Veränderlichen dargestellt werden kann als ein product aus linearen functionen derselben Veränderlichen
    • K. Weierstrass Neuer Beweis des satzes, dass jede ganze rationale function einer Veränderlichen dargestellt werden kann als ein product aus linearen functionen derselben Veränderlichen Sitzungsber. K. Preuss. Akad. Wiss. (Berlin) 1891 1085 1101
    • (1891) Sitzungsber. K. Preuss. Akad. Wiss. (Berlin) , pp. 1085-1101
    • Weierstrass, K.1
  • 22
    • 0001382186 scopus 로고
    • The theory of Smale's point estimation and the convergence of Durand-Kerner program
    • (in Chinese)
    • F. Zhao, and D. Wang The theory of Smale's point estimation and the convergence of Durand-Kerner program Math. Numer. Sin. 15 1993 196 206 (in Chinese)
    • (1993) Math. Numer. Sin. , vol.15 , pp. 196-206
    • Zhao, F.1    Wang, D.2
  • 23
    • 0004429375 scopus 로고
    • On convergence of the Durand-Kerner's method for finding all roots of a polynomial simultaneously
    • S. Zheng On convergence of the Durand-Kerner's method for finding all roots of a polynomial simultaneously Kexue Tongbao 27 1982 1262 1265
    • (1982) Kexue Tongbao , vol.27 , pp. 1262-1265
    • Zheng, S.1
  • 24
    • 84897402289 scopus 로고
    • On convergence of a parallel algorithm for finding the roots of a polynomial
    • (in Chinese)
    • S. Zheng On convergence of a parallel algorithm for finding the roots of a polynomial J. Math. Res. Exposition 7 1987 657 660 (in Chinese)
    • (1987) J. Math. Res. Exposition , vol.7 , pp. 657-660
    • Zheng, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.