메뉴 건너뛰기




Volumn 34, Issue 10, 1997, Pages 49-59

A family of simultaneous zero-finding methods

Author keywords

Convergence order; Iteration functions; Simultaneous methods; Zeros of polynomials

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ITERATIVE METHODS; POLYNOMIALS; PROBLEM SOLVING;

EID: 0031272653     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(97)00206-X     Document Type: Article
Times cited : (25)

References (19)
  • 1
    • 0003275962 scopus 로고
    • A family of root finding methods
    • E. Hansen and M. Patrick, A family of root finding methods, Numer. Math. 27, 257-269, (1977).
    • (1977) Numer. Math. , vol.27 , pp. 257-269
    • Hansen, E.1    Patrick, M.2
  • 2
    • 34447609127 scopus 로고
    • Über unendlich viele algorithmen zur auflösung der gleichungen
    • E. Schröder, Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann. 2, 317-365, (1870).
    • (1870) Math. Ann. , vol.2 , pp. 317-365
    • Schröder, E.1
  • 3
    • 0000999875 scopus 로고
    • Modified Newton method for the simultaneous approximate calculation of all roots of a given algebraic equation (in Bulgarian)
    • K. Dochev, Modified Newton method for the simultaneous approximate calculation of all roots of a given algebraic equation (in Bulgarian), Mat. Spis. B''lgar. Akad. Nauk 5, 136-139, (1962).
    • (1962) Mat. Spis. B''lgar. Akad. Nauk , vol.5 , pp. 136-139
    • Dochev, K.1
  • 4
    • 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, 290-294, (1966).
    • (1966) Numer. Math. , vol.8 , pp. 290-294
    • Kerner, I.O.1
  • 5
    • 85013558033 scopus 로고
    • Validated computation of polynomial zeros by the Durand-Kerner method
    • Edited by J. Herzberger, Elsevier Science B.V.
    • T. Yamamoto, S. Kanno and L. Atanassova, Validated computation of polynomial zeros by the Durand-Kerner method, In Topics in Validated Computations, (Edited by J. Herzberger), pp. 27-53, Elsevier Science B.V., (1994).
    • (1994) Topics in Validated Computations , pp. 27-53
    • Yamamoto, T.1    Kanno, S.2    Atanassova, L.3
  • 6
    • 0000768328 scopus 로고
    • Neuer Beweis des Satzes, dass jede ganze rationale funktion einer veränderlichen dargestellt werden kann als ein produkt aus linearen funktionen derselben veränderlichen
    • Johnson Reprint Corp., New York 1903
    • K. Weierstrass, Neuer Beweis des Satzes, dass jede ganze rationale Funktion einer Veränderlichen dargestellt werden kann als ein Produkt aus linearen Funktionen derselben Veränderlichen, Ges. Werke 3 (Johnson Reprint Corp., New York 1967), 251-269, (1903).
    • (1967) Ges. Werke , vol.3 , pp. 251-269
    • Weierstrass, K.1
  • 8
    • 0021291056 scopus 로고
    • A parallel algorithm for simple roots of polynomials
    • G.H. Ellis and L.T. Watson, A parallel algorithm for simple roots of polynomials, Computers Math. Applic. 10 (2), 107-121, (1984).
    • (1984) Computers Math. Applic. , vol.10 , Issue.2 , pp. 107-121
    • Ellis, G.H.1    Watson, L.T.2
  • 9
    • 34250500064 scopus 로고
    • Residuenabschätzung für polynom-nullstellen mittels lagrange-interpolation
    • W. Börsch-Supan, Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation, Numer. Math. 14, 287-296, (1970).
    • (1970) Numer. Math. , vol.14 , pp. 287-296
    • Börsch-Supan, W.1
  • 10
    • 0030213917 scopus 로고
    • On some simultaneous methods based on Weierstrass' correction
    • T. Sakurai and M.S. Petković, On some simultaneous methods based on Weierstrass' correction, J. Comput. Appl. Math. 72, 275-291, (1995).
    • (1995) J. Comput. Appl. Math. , vol.72 , pp. 275-291
    • Sakurai, T.1    Petković, M.S.2
  • 11
    • 0001102504 scopus 로고
    • Parallel Laguerre iterations: The complex case
    • I. Gargantini, Parallel Laguerre iterations: The complex case, Numer. Math. 26, 317-323, (1976).
    • (1976) Numer. Math. , vol.26 , pp. 317-323
    • Gargantini, I.1
  • 12
    • 0022717371 scopus 로고
    • On some improvements of square root iteration for polynomial zeros
    • M.S. Petković and L.V. Stefanović, On some improvements of square root iteration for polynomial zeros, J. Comput. Appl. Math. 15, 13-25, (1986).
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 13-25
    • Petković, M.S.1    Stefanović, L.V.2
  • 13
    • 38149144227 scopus 로고
    • A high-order iterative formula for simultaneous determination of zeros of a polynomial
    • T. Sakurai, T. Torii and H. Sugiura, A high-order iterative formula for simultaneous determination of zeros of a polynomial, J. Comput. Appl. Math. 38, 387-397, (1991).
    • (1991) J. Comput. Appl. Math. , vol.38 , pp. 387-397
    • Sakurai, T.1    Torii, T.2    Sugiura, H.3
  • 14
    • 0001375526 scopus 로고
    • Further applications of circular arithmetic: Schroeder-like algorithms with error bounds for finding zeros of polynomials
    • I. Gargantini, Further applications of circular arithmetic: Schroeder-like algorithms with error bounds for finding zeros of polynomials, SIAM J. Numer. Anal. 15, 497-510, (1979).
    • (1979) SIAM J. Numer. Anal. , vol.15 , pp. 497-510
    • Gargantini, I.1
  • 15
    • 84966230222 scopus 로고
    • Iteration methods for finding all zeros of a polynomial simultaneously
    • O. Aberth, Iteration methods for finding all zeros of a polynomial simultaneously, Math. Comp. 27, 339-344, (1973).
    • (1973) Math. Comp. , vol.27 , pp. 339-344
    • Aberth, O.1
  • 16
    • 0002770849 scopus 로고
    • A modified Newton method for polynomials
    • L.W. Ehrlich, A modified Newton method for polynomials, Comm. ACM 10, 107-108, (1967).
    • (1967) Comm. ACM , vol.10 , pp. 107-108
    • Ehrlich, L.W.1
  • 17
    • 0000430655 scopus 로고
    • Zur iterativen auflösung algebraischer gleichungen
    • V. H. Maehly, Zur iterativen Auflösung algebraischer Gleichungen, Z. Angew. Math. Phys. 5, 260-263, (1954).
    • (1954) Z. Angew. Math. Phys. , vol.5 , pp. 260-263
    • Maehly, V.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.