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Volumn 62, Issue 2, 1999, Pages 129-145

Modification of Newton's method for analytic mappings having multiple zeros

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; POLES AND ZEROS;

EID: 0032625793     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006070050017     Document Type: Article
Times cited : (13)

References (43)
  • 2
    • 84893197133 scopus 로고
    • Iteration of meromorphic functions
    • Bergweiler, W.: Iteration of meromorphic functions. Bull. Am. Math. Soc. 29, 151-188 (1993).
    • (1993) Bull. Am. Math. Soc. , vol.29 , pp. 151-188
    • Bergweiler, W.1
  • 3
    • 84968494997 scopus 로고
    • Complex analytic dynamics on the Riemann sphere
    • Blanchard, P.: Complex analytic dynamics on the Riemann sphere. Bull. Amer. Math. Soc. 11, 85-141 (1984).
    • (1984) Bull. Amer. Math. Soc. , vol.11 , pp. 85-141
    • Blanchard, P.1
  • 4
    • 0001261109 scopus 로고
    • Convergence rates for Newton's method at singular points
    • Decker, D. W., Keller, H. B., Kelley, C. T.: Convergence rates for Newton's method at singular points. SIAM J. Numer. Anal. 20, 296-314 (1983).
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 296-314
    • Decker, D.W.1    Keller, H.B.2    Kelley, C.T.3
  • 5
    • 0002689824 scopus 로고
    • Newton's method at singular points: I
    • Decker, D. W., Kelley, C. T.: Newton's method at singular points: I. SIAM J. Numer. Anal. 17, 66-70 (1980).
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 66-70
    • Decker, D.W.1    Kelley, C.T.2
  • 6
    • 0002689826 scopus 로고
    • Newton's method at singular points: II
    • Decker, D. W., Kelley, C. T.: Newton's method at singular points: II. SIAM J. Numer. Anal. 17, 465-471 (1980).
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 465-471
    • Decker, D.W.1    Kelley, C.T.2
  • 7
    • 0000271531 scopus 로고
    • Convergence acceleration for Newton's method at singular points
    • Decker, D. W., Kelley, C. T.: Convergence acceleration for Newton's method at singular points. SIAM J. Numer. Anal. 19, 219-229 (1981).
    • (1981) SIAM J. Numer. Anal. , vol.19 , pp. 219-229
    • Decker, D.W.1    Kelley, C.T.2
  • 8
    • 0022076101 scopus 로고
    • Broyden's method for a class of problems having singular Jacobian at the root
    • Decker, D. W., Kelley, C. T.: Broyden's method for a class of problems having singular Jacobian at the root. SIAM J. Numer. Anal. 22, 566-574 (1985).
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 566-574
    • Decker, D.W.1    Kelley, C.T.2
  • 9
    • 0008865344 scopus 로고
    • Expanded convergence domains for Newton's method at nearly singular roots
    • Decker, D. W., Kelley, C. T.: Expanded convergence domains for Newton's method at nearly singular roots. SIAM J. Sci. Stat. Comput. 6, 951-966 (1985).
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 951-966
    • Decker, D.W.1    Kelley, C.T.2
  • 10
    • 0002399441 scopus 로고
    • Starlike domains of convergence for Newton's method at singularities
    • Griewank, A.: Starlike domains of convergence for Newton's method at singularities. Numer. Math. 35, 95-111 (1980).
    • (1980) Numer. Math. , vol.35 , pp. 95-111
    • Griewank, A.1
  • 11
    • 0022384709 scopus 로고
    • On solving nonlinear equations with simple singularities or nearly singular solutions
    • Griewank, A.: On solving nonlinear equations with simple singularities or nearly singular solutions. SIAM Rev. 27, 537-563 (1985).
    • (1985) SIAM Rev. , vol.27 , pp. 537-563
    • Griewank, A.1
  • 12
    • 0010833281 scopus 로고
    • Newton's method for singular problems when the dimension of the null space is > 1
    • Griewank, A., Osborne, M. R.: Newton's method for singular problems when the dimension of the null space is > 1. SIAM J. Numer. Anal. 18, 145-149 (1981).
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 145-149
    • Griewank, A.1    Osborne, M.R.2
  • 13
    • 0001587909 scopus 로고
    • Analysis of Newton's method at irregular singularities
    • Griewank, A., Osborne, M. R.: Analysis of Newton's method at irregular singularities. SIAM J. Numer. Anal. 20, 747-773 (1983).
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 747-773
    • Griewank, A.1    Osborne, M.R.2
  • 14
    • 0023827171 scopus 로고
    • A relation between Newton and Gauss-Newton steps for singular nonlinear equations
    • Hoy, A.: A relation between Newton and Gauss-Newton steps for singular nonlinear equations. Computing 40, 19-27 (1988).
    • (1988) Computing , vol.40 , pp. 19-27
    • Hoy, A.1
  • 15
    • 0040248799 scopus 로고
    • An efficiently implementable Gauss-Newton-like method for solving singular nonlinear equations
    • Hoy, A.: An efficiently implementable Gauss-Newton-like method for solving singular nonlinear equations. Computing 41, 107-122 (1989).
    • (1989) Computing , vol.41 , pp. 107-122
    • Hoy, A.1
  • 16
    • 0040248785 scopus 로고
    • Some superlinearly convergent methods for solving singular nonlinear equations
    • (Allgower, E. L., Georg, K., eds.), Rhode Island: SIAM
    • Hoy, A., Schwetlick, H.: Some superlinearly convergent methods for solving singular nonlinear equations. In: Computational solution of nonlinear systems of equations (Allgower, E. L., Georg, K., eds.), pp. 285-300. Rhode Island: SIAM, 1990.
    • (1990) Computational Solution of Nonlinear Systems of Equations , pp. 285-300
    • Hoy, A.1    Schwetlick, H.2
  • 17
    • 0000220426 scopus 로고
    • Geometrically isolated nonisolated solutions and their approximation
    • Keller, H. B.: Geometrically isolated nonisolated solutions and their approximation. SIAM J. Numer. Anal. 18, 822-838 (1981).
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 822-838
    • Keller, H.B.1
  • 18
    • 84966213341 scopus 로고
    • A shamanskii-like acceleration scheme for nonlinear equations at singular roots
    • Kelley, C. T.: A Shamanskii-like acceleration scheme for nonlinear equations at singular roots. Math. Comput. 47, 609-623 (1986).
    • (1986) Math. Comput. , vol.47 , pp. 609-623
    • Kelley, C.T.1
  • 19
    • 0001261107 scopus 로고
    • A new acceleration method for Newton's method at singular points
    • Kelley, C. T., Suresh, R.: A new acceleration method for Newton's method at singular points. SIAM J. Numer. Anal. 20, 1001-1009 (1983).
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 1001-1009
    • Kelley, C.T.1    Suresh, R.2
  • 20
    • 0020649428 scopus 로고
    • Improving the Van de Vel root-finding method
    • King, R. F.: Improving the Van de Vel root-finding method. Computing 30, 373-378 (1983).
    • (1983) Computing , vol.30 , pp. 373-378
    • King, R.F.1
  • 21
    • 0039049330 scopus 로고
    • Efficient computation of singular points
    • Kunkel, P.: Efficient computation of singular points. IMA J. Numer. Anal. 9, 421-433 (1989).
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 421-433
    • Kunkel, P.1
  • 22
    • 0025661616 scopus 로고
    • A special extended system and a Newton-like method for simple singular nonlinear equations
    • Mei, Z.: A special extended system and a Newton-like method for simple singular nonlinear equations. Computing 45, 157-167 (1990).
    • (1990) Computing , vol.45 , pp. 157-167
    • Mei, Z.1
  • 24
    • 0021212596 scopus 로고
    • A quadratically convergent method for computing simple singular roots and its application to determining simple bifurcation points
    • Menzel, R., Pönisch, G.: A quadratically convergent method for computing simple singular roots and its application to determining simple bifurcation points. Computing 32, 127-138 (1984).
    • (1984) Computing , vol.32 , pp. 127-138
    • Menzel, R.1    Pönisch, G.2
  • 25
    • 34249955199 scopus 로고
    • Computing singular solutions to nonlinear analytic systems
    • Morgan, A. P., Sommese, A. J., Wampler, C. W.: Computing singular solutions to nonlinear analytic systems. Numer. Math. 58, 669-684 (1991).
    • (1991) Numer. Math. , vol.58 , pp. 669-684
    • Morgan, A.P.1    Sommese, A.J.2    Wampler, C.W.3
  • 26
    • 0012217753 scopus 로고
    • Computing singular solutions to polynomial systems
    • Morgan, A. P., Sommese, A. J., Wampler, C. W.: Computing singular solutions to polynomial systems. Adv. Appl. Math. 13, 305-327 (1992).
    • (1992) Adv. Appl. Math. , vol.13 , pp. 305-327
    • Morgan, A.P.1    Sommese, A.J.2    Wampler, C.W.3
  • 27
    • 21144479938 scopus 로고
    • A power series method for computing singular solutions to nonlinear analytic systems
    • Morgan, A. P., Sommese, A. J., Wampler, C. W.: A power series method for computing singular solutions to nonlinear analytic systems. Numer. Math. 63, 391-409 (1992).
    • (1992) Numer. Math. , vol.63 , pp. 391-409
    • Morgan, A.P.1    Sommese, A.J.2    Wampler, C.W.3
  • 28
    • 21344485372 scopus 로고
    • Convergence of Newton-like methods for singular operator equations using outer inverses
    • Nashed, M. Z., Chen, X.: Convergence of Newton-like methods for singular operator equations using outer inverses. Numer. Math. 66, 235-257 (1993).
    • (1993) Numer. Math. , vol.66 , pp. 235-257
    • Nashed, M.Z.1    Chen, X.2
  • 29
    • 0021124189 scopus 로고
    • A higher order method for determining nonisolated solutions of a system of nonlinear equations
    • Neta, B., Victory, H. D.: A higher order method for determining nonisolated solutions of a system of nonlinear equations. Computing 32, 163-166 (1984).
    • (1984) Computing , vol.32 , pp. 163-166
    • Neta, B.1    Victory, H.D.2
  • 30
    • 0023329339 scopus 로고
    • Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations
    • Ojika, T.: Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations. J. Math. Anal. Appl. 123, 199-221 (1987).
    • (1987) J. Math. Anal. Appl. , vol.123 , pp. 199-221
    • Ojika, T.1
  • 31
    • 0023329415 scopus 로고
    • Modified deflation algorithm for the solution of singular problems. II. Nonlinear multipoint boundary value problems
    • Ojika, T.: Modified deflation algorithm for the solution of singular problems. II. Nonlinear multipoint boundary value problems. J. Math. Anal. Appl. 123, 222-237 (1987).
    • (1987) J. Math. Anal. Appl. , vol.123 , pp. 222-237
    • Ojika, T.1
  • 32
    • 0020830979 scopus 로고
    • Deflation algorithm for the multiple roots of a system of nonlinear equations
    • Ojika, T., Watanabe, S., Mitsui, T.: Deflation algorithm for the multiple roots of a system of nonlinear equations. J. Math. Anal. Appl. 96, 463-479 (1983).
    • (1983) J. Math. Anal. Appl. , vol.96 , pp. 463-479
    • Ojika, T.1    Watanabe, S.2    Mitsui, T.3
  • 33
    • 0001482673 scopus 로고
    • Global aspects of the continuous and discrete Newton method: A case study
    • Peitgen, H.-O., Prüfer, M., Schmitt, K.: Global aspects of the continuous and discrete Newton method: A case study. Acta Appl. Math. 13, 123-202 (1988).
    • (1988) Acta Appl. Math. , vol.13 , pp. 123-202
    • Peitgen, H.-O.1    Prüfer, M.2    Schmitt, K.3
  • 34
    • 0001920382 scopus 로고
    • Convergence of the Newton process to multiple solutions
    • Rall, L. B.: Convergence of the Newton process to multiple solutions. Numer. Math. 9, 23-37 (1966).
    • (1966) Numer. Math. , vol.9 , pp. 23-37
    • Rall, L.B.1
  • 35
    • 0001281959 scopus 로고
    • On Newton's method for singular problems
    • Reddien, G. W.: On Newton's method for singular problems. SIAM J. Numer. Anal. 15, 993-996 (1978).
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 993-996
    • Reddien, G.W.1
  • 36
    • 0018688384 scopus 로고
    • Newton's method and high order singularities
    • Reddien, G. W.: Newton's method and high order singularities. Comput. Math. Appl. 5, 79-86 (1979).
    • (1979) Comput. Math. Appl. , vol.5 , pp. 79-86
    • Reddien, G.W.1
  • 38
    • 0004604130 scopus 로고
    • Enlargement procedure for resolution of singularities at simple singular solutions of nonlinear equations
    • Tsuchiya, T.: Enlargement procedure for resolution of singularities at simple singular solutions of nonlinear equations. Numer. Math. 52, 401-411 (1988).
    • (1988) Numer. Math. , vol.52 , pp. 401-411
    • Tsuchiya, T.1
  • 39
    • 0002477442 scopus 로고
    • Newton's method and complex dynamical systems
    • Haeseler, F. v., Peitgen, H.-O.: Newton's method and complex dynamical systems. Acta Appl. Mat. 13, 3-58 (1988).
    • (1988) Acta Appl. Mat. , vol.13 , pp. 3-58
    • Haeseler, F.V.1    Peitgen, H.-O.2
  • 40
    • 0016459272 scopus 로고
    • A method for computing a root of a single nonlinear equation, including its multiplicity
    • Vel, H. Van de: A method for computing a root of a single nonlinear equation, including its multiplicity. Computing 14, 167-171 (1975).
    • (1975) Computing , vol.14 , pp. 167-171
    • Van De Vel, H.1
  • 42
    • 0019668490 scopus 로고
    • On the accurate determination of nonisolated solutions of nonlinear equations
    • Weber, H., Werner, W.: On the accurate determination of nonisolated solutions of nonlinear equations. Computing 26, 315-326 (1981).
    • (1981) Computing , vol.26 , pp. 315-326
    • Weber, H.1    Werner, W.2
  • 43
    • 0020786173 scopus 로고
    • Finding a multiple zero by transformations and Newton-like methods
    • Ypma, T. J.: 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.J.1


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