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Volumn 54, Issue 2, 2010, Pages 219-243

A study of accelerated Newton methods for multiple polynomial roots

Author keywords

Convergence acceleration; Multiple zeros; Multiplicity estimates; Newton method; Polynomials

Indexed keywords


EID: 77952107147     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-009-9332-x     Document Type: Article
Times cited : (12)

References (34)
  • 1
    • 0040802647 scopus 로고
    • On types of convergence and behavior of approximations in the neighborhood of a multiple root of an equation
    • Bodewig, E.: On types of convergence and behavior of approximations in the neighborhood of a multiple root of an equation. Q. Appl. Math. 7, 325-333 (1949).
    • (1949) Q. Appl. Math. , vol.7 , pp. 325-333
    • Bodewig, E.1
  • 2
    • 34250270406 scopus 로고
    • A note on the computation of multiple zeros of polynomial by Newton's method
    • Channabasappa, M.: A note on the computation of multiple zeros of polynomial by Newton's method. BIT 19, 134-135 (1979).
    • (1979) BIT , vol.19 , pp. 134-135
    • Channabasappa, M.1
  • 3
    • 77952104826 scopus 로고
    • Roots of Polynomials by Ratio of Successive Derivatives
    • NASA, Washington
    • Crouse, J. E., Putt, C. W.: Roots of Polynomials by Ratio of Successive Derivatives. Technical Report, NASA TN D-6793, NASA, Washington (1972).
    • (1972) Technical Report, NASA TN D-6793
    • Crouse, J.E.1    Putt, C.W.2
  • 5
    • 34250392602 scopus 로고
    • Estimating the multiplicity of a root
    • Hansen, E., Patrick, M.: Estimating the multiplicity of a root. Numer. Math. 27, 121-131 (1976).
    • (1976) Numer. Math. , vol.27 , pp. 121-131
    • Hansen, E.1    Patrick, M.2
  • 7
    • 0001440927 scopus 로고
    • A note on Halley's method
    • Hernández Verón, M. A.: A note on Halley's method. Numer. Math. 59, 273-276 (1991).
    • (1991) Numer. Math. , vol.59 , pp. 273-276
    • Hernández Verón, M.A.1
  • 10
    • 0030244864 scopus 로고    scopus 로고
    • The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence
    • Hull, T. E., Mathon, R.: The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence. ACM Trans. Math. Softw. 22, 261-280 (1996).
    • (1996) ACM Trans. Math. Softw. , vol.22 , pp. 261-280
    • Hull, T.E.1    Mathon, R.2
  • 11
    • 0039024273 scopus 로고
    • Relationships between order and efficiency of a class of methods for multiple zero of polynomials
    • Igarashi, M., Ypma, T.: Relationships between order and efficiency of a class of methods for multiple zero of polynomials. J. Comput. Appl. Math. 60, 101-113 (1995).
    • (1995) J. Comput. Appl. Math. , vol.60 , pp. 101-113
    • Igarashi, M.1    Ypma, T.2
  • 12
    • 0043233722 scopus 로고    scopus 로고
    • Empirical versus asymptotic rate of convergence of a class of methods for solving polynomial equations
    • Igarashi, M., Ypma, T.: Empirical versus asymptotic rate of convergence of a class of methods for solving polynomial equations. J. Comput. Appl. Math. 82, 229-237 (1997).
    • (1997) J. Comput. Appl. Math. , vol.82 , pp. 229-237
    • Igarashi, M.1    Ypma, T.2
  • 13
    • 84919055665 scopus 로고
    • Principles for testing polynomial zerofinding programs
    • Jenkins, M., Traub, J.: Principles for testing polynomial zerofinding programs. ACM Trans. Math. Softw. 1, 26-34 (1975).
    • (1975) ACM Trans. Math. Softw. , vol.1 , pp. 26-34
    • Jenkins, M.1    Traub, J.2
  • 15
    • 0020649428 scopus 로고
    • Improving the Van de Vel Root-Finding method
    • King, R.: Improving the van de Vel Root-Finding method. Computing 30, 373-378 (1983).
    • (1983) Computing , vol.30 , pp. 373-378
    • King, R.1
  • 16
    • 0032625793 scopus 로고    scopus 로고
    • A modification of Newton's method for analytic mappings having multiple zeros
    • Kravanja, P., Haegemans, A.: A modification of Newton's method for analytic mappings having multiple zeros. Computing 62, 129-145 (1999).
    • (1999) Computing , vol.62 , pp. 129-145
    • Kravanja, P.1    Haegemans, A.2
  • 18
    • 77952101350 scopus 로고
    • A New and Efficient Program for Finding All Polynomial Roots
    • Rice University, Houston
    • Lang, M., Frenzel, B. C.: A New and Efficient Program for Finding All Polynomial Roots. Technical Report #9308, Rice University, Houston (1994).
    • (1994) Technical Report #9308
    • Lang, M.1    Frenzel, B.C.2
  • 19
    • 0346244430 scopus 로고
    • A root-finding algorithm based on Newton's method
    • Madsen, K.: A root-finding algorithm based on Newton's method. BIT 13, 71-75 (1973).
    • (1973) BIT , vol.13 , pp. 71-75
    • Madsen, K.1
  • 20
    • 0347703690 scopus 로고
    • FORTRAN Subroutines for Finding Polynomial Zeros
    • Computer Science and System Division, A.E.R.E. Harwell, Oxfordshire
    • Madsen, K., Reid, J. K.: FORTRAN Subroutines for Finding Polynomial Zeros. Technical Report A. E. R. E. R. 7986, Computer Science and System Division, A. E. R. E. Harwell, Oxfordshire (1975).
    • (1975) Technical Report A.E.R.E.R. 7986
    • Madsen, K.1    Reid, J.K.2
  • 21
    • 77952111600 scopus 로고
    • An improved Newton's method
    • Mathews, J. H.: An improved Newton's method. AMATYC Rev. 10, 9-14 (1989).
    • (1989) AMATYC Rev. , vol.10 , pp. 9-14
    • Mathews, J.H.1
  • 22
    • 0347718223 scopus 로고    scopus 로고
    • A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots
    • McNamee, J.: A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots. ACM SIGNUM Newsl. 33, 17-22 (1998).
    • (1998) ACM SIGNUM Newsl. , vol.33 , pp. 17-22
    • McNamee, J.1
  • 24
    • 0032183498 scopus 로고    scopus 로고
    • Improving the order of convergence of iteration functions
    • Osada, N.: Improving the order of convergence of iteration functions. J. Comput. Appl. Math. 98, 311-315 (1998).
    • (1998) J. Comput. Appl. Math. , vol.98 , pp. 311-315
    • Osada, N.1
  • 26
    • 0001920382 scopus 로고
    • Convergence of the Newton process to multiple solutions
    • Rall, L.: Convergence of the Newton process to multiple solutions. Numer. Math. 9, 23-37 (1966).
    • (1966) Numer. Math. , vol.9 , pp. 23-37
    • Rall, L.1
  • 27
    • 34447609127 scopus 로고
    • Über unendlich viele Algorithmen zur Auflösung der Gleichungen
    • English translation by G.W. Stewart: On Infinitely Many Algorithms for Solving Equations. Technical Report TR-92-121, University of Maryland, Department of Computer Science (1992)
    • Schröder, E.: Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Math. Ann. 2, 317-365 (1870). English translation by G. W. Stewart: On Infinitely Many Algorithms for Solving Equations. Technical Report TR-92-121, University of Maryland, Department of Computer Science (1992).
    • (1870) Math. Ann. , vol.2 , pp. 317-365
    • Schröder, E.1
  • 29
    • 0344440523 scopus 로고
    • The behavior of a multiplicity independent root-finding scheme in the presence of error
    • Stewart, G.: The behavior of a multiplicity independent root-finding scheme in the presence of error. BIT 20, 526-528 (1980).
    • (1980) BIT , vol.20 , pp. 526-528
    • Stewart, G.1
  • 31
    • 0016459272 scopus 로고
    • A method for computing a root of a single nonlinear equation, including its multiplicity
    • van de Vel, H.: A method for computing a root of a single nonlinear equation, including its multiplicity. Computing 14, 167-171 (1974).
    • (1974) Computing , vol.14 , pp. 167-171
    • van de Vel, H.1
  • 32
    • 0020786173 scopus 로고
    • Finding a multiple zero by transformations and Newton-like methods
    • Ypma, T.: Finding a multiple zero by transformations and Newton-like methods. SIAM Rev. 25, 365-378 (1983).
    • (1983) SIAM Rev. , vol.25 , pp. 365-378
    • Ypma, T.1
  • 33
    • 14944343328 scopus 로고    scopus 로고
    • Computing multiple roots of inexact polynomials
    • Zeng, Z.: Computing multiple roots of inexact polynomials. Math. Comput. 74, 869-903 (2004).
    • (2004) Math. Comput. , vol.74 , pp. 869-903
    • Zeng, Z.1
  • 34
    • 2942692216 scopus 로고    scopus 로고
    • Algorithm 835: MULTROOT-a Matlab package for computing polynomial roots and multiplicities
    • Zeng, Z.: Algorithm 835: MULTROOT-a Matlab package for computing polynomial roots and multiplicities. ACM Trans. Math. Softw. 30, 218-236 (2004).
    • (2004) ACM Trans. Math. Softw. , vol.30 , pp. 218-236
    • Zeng, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.