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Volumn 39, Issue 6, 2007, Pages 649-659

Finding all solutions of systems of nonlinear equations with free variables

Author keywords

Free variables; Global optimization; Systems of nonlinear equations

Indexed keywords

ENGINEERING EDUCATION; GLOBAL OPTIMIZATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 34547292695     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/03052150701243853     Document Type: Article
Times cited : (9)

References (22)
  • 1
    • 28344437926 scopus 로고    scopus 로고
    • Solution of bounded nonlinear systems of equations using homotopies with inexact restoration
    • Birgin, E.G., Krejíc, N. and Martínez, J.M., Solution of bounded nonlinear systems of equations using homotopies with inexact restoration. Int. J. Comput. Math., 2003, 80, 211-222.
    • (2003) Int. J. Comput. Math , vol.80 , pp. 211-222
    • Birgin, E.G.1    Krejíc, N.2    Martínez, J.M.3
  • 2
    • 0041148162 scopus 로고
    • Solving systems of equations
    • Newsgroup Article 3529
    • Boon, S., Solving systems of equations. Sci. Math. Num-Analysis, 1992, Newsgroup Article 3529.
    • (1992) Sci. Math. Num-Analysis
    • Boon, S.1
  • 3
    • 0028445933 scopus 로고
    • The monomial method: Extensions, variations, and performance issues
    • Burns, S.A., The monomial method: extensions, variations, and performance issues. Int. J. Num. Methods Eng., 1994, 37, 2093-2107.
    • (1994) Int. J. Num. Methods Eng , vol.37 , pp. 2093-2107
    • Burns, S.A.1
  • 4
    • 0026153412 scopus 로고
    • A monomial-based method for solving systems of non-linear algebraic equations
    • Burns, S.A. and Locascio, A., A monomial-based method for solving systems of non-linear algebraic equations. Int. J. Num. Methods Eng., 1991, 31, 1295-1318.
    • (1991) Int. J. Num. Methods Eng , vol.31 , pp. 1295-1318
    • Burns, S.A.1    Locascio, A.2
  • 5
    • 0035568530 scopus 로고    scopus 로고
    • Design of civil engineering frame structures using a monomial/newton hybrid method
    • Burns, S.A. and Mueller, K.M., Design of civil engineering frame structures using a monomial/newton hybrid method. Ann. Operat. Res., 2001, 105, 21-35.
    • (2001) Ann. Operat. Res , vol.105 , pp. 21-35
    • Burns, S.A.1    Mueller, K.M.2
  • 6
    • 0021202727 scopus 로고
    • On solving large sparse nonlinear equation systems
    • Chen, H.S. and Stadtherr, M.A., On solving large sparse nonlinear equation systems. Comput. Chem. Eng., 1984, 8, 1-7.
    • (1984) Comput. Chem. Eng , vol.8 , pp. 1-7
    • Chen, H.S.1    Stadtherr, M.A.2
  • 7
    • 0011359978 scopus 로고
    • The use of linear programming for the solution of sparse sets of nonlinear equations
    • Duff, I.S., Nocedal, J. and Reid, J.K., The use of linear programming for the solution of sparse sets of nonlinear equations. SIAM J. Sci. Stat. Comput., 1987, 8, 99-108.
    • (1987) SIAM J. Sci. Stat. Comput , vol.8 , pp. 99-108
    • Duff, I.S.1    Nocedal, J.2    Reid, J.K.3
  • 8
    • 0000440753 scopus 로고    scopus 로고
    • Recent advances in global optimization for process synthesis, design and control: Enclosure of all solutions
    • Floudas, C.A., Recent advances in global optimization for process synthesis, design and control: enclosure of all solutions. Comput. Chem. Eng., 1999, Supplement, S963-973.
    • (1999) Comput. Chem. Eng , Issue.SUPPL.EMENT
    • Floudas, C.A.1
  • 10
    • 0036680974 scopus 로고    scopus 로고
    • Approximately global optimization for assortment problems using piecewise linearization techniques
    • Li, H.L., Chang, C.T. and Tsai, J.F., Approximately global optimization for assortment problems using piecewise linearization techniques. Eur. J. Operat. Res., 2002, 140, 584-589.
    • (2002) Eur. J. Operat. Res , vol.140 , pp. 584-589
    • Li, H.L.1    Chang, C.T.2    Tsai, J.F.3
  • 11
    • 34547302714 scopus 로고    scopus 로고
    • LINGO Release 9.0. LINDO System Inc, Chicago, 2004
    • LINGO Release 9.0. LINDO System Inc., Chicago, 2004.
  • 12
    • 34249758275 scopus 로고
    • Finding all solutions of nonlinearly constrained systems of equations
    • Maranas, C.D. and Floudas, C.A., Finding all solutions of nonlinearly constrained systems of equations. J. Global Optimiz., 1995, 7, 143-182.
    • (1995) J. Global Optimiz , vol.7 , pp. 143-182
    • Maranas, C.D.1    Floudas, C.A.2
  • 13
    • 0001743879 scopus 로고
    • Bounded homotopies to solve systems of algebraic nonlinear equations
    • Paloschi, J.R., Bounded homotopies to solve systems of algebraic nonlinear equations. Comput. Chem. Eng., 1995, 19, 1243-1254.
    • (1995) Comput. Chem. Eng , vol.19 , pp. 1243-1254
    • Paloschi, J.R.1
  • 14
    • 0030652720 scopus 로고    scopus 로고
    • Bounded homotopies to solve systems of sparse algebraic nonlinear equations
    • Paloschi, J.R., Bounded homotopies to solve systems of sparse algebraic nonlinear equations. Comput. Chem. Eng., 1997, 21, 531-541.
    • (1997) Comput. Chem. Eng , vol.21 , pp. 531-541
    • Paloschi, J.R.1
  • 15
    • 0002626123 scopus 로고
    • A hybrid method for nonlinear equations
    • edited by P. Rabinowitz, Gordon and Breach: London
    • Powell, M J.D., A hybrid method for nonlinear equations. In Numerical Methods for Nonlinear Algebraic Equations. edited by P. Rabinowitz, 1970 (Gordon and Breach: London).
    • (1970) Numerical Methods for Nonlinear Algebraic Equations
    • Powell, M.J.D.1
  • 18
    • 20444499467 scopus 로고    scopus 로고
    • Global optimization for nonlinear fractional programming problems in engineering design
    • Tsai, J.F., Global optimization for nonlinear fractional programming problems in engineering design. Eng. Optimiz., 2005, 37, 399-409.
    • (2005) Eng. Optimiz , vol.37 , pp. 399-409
    • Tsai, J.F.1
  • 19
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795 : PHCpack: A general-purpose solver for polynomial systems by homotopy continuation
    • Verschelde, J., Algorithm 795 : PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Software, 1999, 25, 251-276.
    • (1999) ACM Trans. Math. Software , vol.25 , pp. 251-276
    • Verschelde, J.1
  • 20
    • 0000900077 scopus 로고    scopus 로고
    • Finding all solutions of nonlinear equations using linear combinations of functions
    • Yamamura, K., Finding all solutions of nonlinear equations using linear combinations of functions. Reliable Comput., 2000, 6, 105-113.
    • (2000) Reliable Comput , vol.6 , pp. 105-113
    • Yamamura, K.1
  • 21
    • 0012216756 scopus 로고    scopus 로고
    • Finding all solutions of systems of nonlinear equations using the dual simplex method
    • Yamamura, K. and Tanaka, S. Finding all solutions of systems of nonlinear equations using the dual simplex method. BIT Num. Math., 2002, 42, 214-230.
    • (2002) BIT Num. Math , vol.42 , pp. 214-230
    • Yamamura, K.1    Tanaka, S.2
  • 22
    • 0001601527 scopus 로고    scopus 로고
    • Interval solution of nonlinear equations using linear programming
    • Yamamura, K., Kawata, H. and Tokue, A., Interval solution of nonlinear equations using linear programming. BIT Num. Math., 1998, 38, 186-199.
    • (1998) BIT Num. Math , vol.38 , pp. 186-199
    • Yamamura, K.1    Kawata, H.2    Tokue, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.