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Volumn 58, Issue 1, 1997, Pages 69-89

Numerical experience with newton-like methods for nonlinear algebraic systems

Author keywords

Attraction region; Broyden's method; Fractal structure; Greenstadt's method; Mart nez' column method; Newton's Method; Nonlinear Huang's method, row update ABS method; Quasi Newton methods; Thomas' method

Indexed keywords

ALGEBRA; FRACTALS; ITERATIVE METHODS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS);

EID: 0030674719     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02684472     Document Type: Article
Times cited : (38)

References (17)
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    • Allgower, E.L.1    Georg, K.2
  • 4
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • Broyden, C. G.: A class of methods for solving nonlinear simultaneous equations. Math. Comp. 19, 577-593 (1965).
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    • Broyden, C.G.1
  • 5
    • 51249188846 scopus 로고
    • A significant example to test methods solving systems of nonlinear equations
    • Gheri, G., Mancino, O. G.: A significant example to test methods solving systems of nonlinear equations. Calcolo 8, 107-114 (1971).
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    • Gheri, G.1    Mancino, O.G.2
  • 6
    • 0028710557 scopus 로고
    • Row update ABS methods for systems of nonlinear equations
    • Huang, Z.: Row update ABS methods for systems of nonlinear equations. Optimiz. Methods Software 3, 41-60 (1994).
    • (1994) Optimiz. Methods Software , vol.3 , pp. 41-60
    • Huang, Z.1
  • 9
    • 0021614679 scopus 로고
    • A quasi-Newton method with modification of one column per iteration
    • Martínez, J. M.: A quasi-Newton method with modification of one column per iteration. Computing 33, 353-362 (1984).
    • (1984) Computing , vol.33 , pp. 353-362
    • Martínez, J.M.1
  • 10
    • 0038411679 scopus 로고
    • Algorithms for solving nonlinear systems of equation
    • (Spedicato, E., ed.), NATO ASI Series, Dordrecht; Kluwer
    • Martínez, J. M.: Algorithms for solving nonlinear systems of equation. In: Algorithms for continuous optimization: the state of the art (Spedicato, E., ed.), NATO ASI Series, Dordrecht; Kluwer 1994.
    • (1994) Algorithms for Continuous Optimization: The State of the Art
    • Martínez, J.M.1
  • 12
    • 0022443028 scopus 로고
    • On the monotone convergence of Newton's method
    • Potra, F. A., Rheinboldt, W. C.: On the monotone convergence of Newton's method. Computing 36, 81-90 (1986).
    • (1986) Computing , vol.36 , pp. 81-90
    • Potra, F.A.1    Rheinboldt, W.C.2
  • 14
    • 0040384921 scopus 로고
    • On the closed form solution of Troesch's problem
    • Roberts, S. M., Shipman, J. S.: On the closed form solution of Troesch's problem. J. Comput. Physics 21, 291-304 (1976).
    • (1976) J. Comput. Physics , vol.21 , pp. 291-304
    • Roberts, S.M.1    Shipman, J.S.2
  • 15
    • 0039087062 scopus 로고
    • On some classes of variationally derived Quasi-Newton algorithms for systems of nonlinear algebraic equation
    • Spedicato, E., Greenstadt, J.: On some classes of variationally derived Quasi-Newton algorithms for systems of nonlinear algebraic equation, Numer. Math, 29, 363-380 (1978).
    • (1978) Numer. Math , vol.29 , pp. 363-380
    • Spedicato, E.1    Greenstadt, J.2
  • 17
    • 84966239647 scopus 로고
    • Numerical solution of large sets of algebraic nonlinear equations
    • Toint, Ph L.: Numerical solution of large sets of algebraic nonlinear equations. Math. Comp. 46, 175-189 (1986).
    • (1986) Math. Comp. , vol.46 , pp. 175-189
    • Toint, Ph.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.