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Volumn 14, Issue 4, 1988, Pages 312-329

Solving Systems of Nonlinear Equations Using the Nonzero Value of the Topological Degree

Author keywords

existence of the solution; generalized method of bisection; isolation of a root; localization of a root; solution of nonlinear systems; topological degree of a mapping

Indexed keywords

MATHEMATICAL TECHNIQUES--NONLINEAR EQUATIONS;

EID: 0024141611     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/50063.214384     Document Type: Article
Times cited : (66)

References (27)
  • 1
    • 0003792627 scopus 로고
    • Springer-Verlag, Berlin, 1935. Reprinted: Chelsea, Bronx, N.Y.
    • Alexandroff, P., and Hopf, H. Topologie. Springer-Verlag, Berlin, 1935. Reprinted: Chelsea, Bronx, N.Y., 1965.
    • (1965) Topologie
    • Alexandroff, P.1    Hopf, H.2
  • 3
    • 0021629874 scopus 로고
    • A bisection method for systems of nonlinear equations
    • Dec.
    • Eiger, A., Sikorski, K., and Stenger, F. A bisection method for systems of nonlinear equations. ACM Trans. Math. Softw. 10, 4 (Dec. 1984), 367–377.
    • (1984) ACM Trans. Math. Softw. , vol.10 , Issue.4 , pp. 367-377
    • Eiger, A.1    Sikorski, K.2    Stenger, F.3
  • 4
    • 0017637514 scopus 로고
    • On the structure of zero finders
    • Gonnet, G. H. On the structure of zero finders. Bit 17 (1977), 170–183.
    • (1977) Bit , vol.17 , pp. 170-183
    • Gonnet, G.H.1
  • 5
    • 84976770856 scopus 로고    scopus 로고
    • The implicit function theorem for solving systems of nonlinear equations in R2
    • To be published.
    • Grapsa, T. N., and Vrahatis, M. N. The implicit function theorem for solving systems of nonlinear equations in R2. Int. J. Comput. Math. To be published.
    • Int. J. Comput. Math.
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 6
    • 0016900156 scopus 로고
    • A two-dimensional analogue to the method of bisections for solving nonlinear equations
    • Harvey, C., and Stenger, F. A two-dimensional analogue to the method of bisections for solving nonlinear equations. Q. Appl. Math. 5, 33 (1976), 351–368.
    • (1976) Q. Appl. Math. , vol.5 , Issue.33 , pp. 351-368
    • Harvey, C.1    Stenger, F.2
  • 8
    • 0000963644 scopus 로고
    • An efficient degree-computation method for a generalized method of bisection
    • Kearfott, R. B. An efficient degree-computation method for a generalized method of bisection. Numer. Math. 32 (1979), 109–127.
    • (1979) Numer. Math. , vol.32 , pp. 109-127
    • Kearfott, R.B.1
  • 9
    • 84966261060 scopus 로고
    • Abstract generalized bisection and a cost bound
    • July
    • Kearfott, R. B. Abstract generalized bisection and a cost bound. Math. Comput. 49,179 (July 1987), 187–202.
    • (1987) Math. Comput. , vol.49 , Issue.179 , pp. 187-202
    • Kearfott, R.B.1
  • 10
    • 0023415987 scopus 로고
    • Some tests of generalized bisection
    • Sept.
    • Kearfott, R. B. Some tests of generalized bisection. ACM Trans. Math. Softw. 13, 3 (Sept. 1987), 197–220.
    • (1987) ACM Trans. Math. Softw. , vol.13 , Issue.3 , pp. 197-220
    • Kearfott, R.B.1
  • 11
    • 0003657590 scopus 로고
    • Vol. 2, Seminumerical Algorithms. Addison-Wesley, Reading, Mass.
    • Knuth, D. E. The Art of Computer Programming. Vol. 2, Seminumerical Algorithms. Addison-Wesley, Reading, Mass., 1969.
    • (1969) The Art of Computer Programming
    • Knuth, D.E.1
  • 12
    • 84976785189 scopus 로고
    • BRENTM, A Fortran subroutine for the numerical solution of systems of nonlinear equations
    • June
    • Moré, J. J., and Cosnard, M. Y. BRENTM, A Fortran subroutine for the numerical solution of systems of nonlinear equations. ACM Trans. Math. Softw. 6, 2 (June 1980), 240–251.
    • (1980) ACM Trans. Math. Softw. , vol.6 , Issue.2 , pp. 240-251
    • Moré, J.J.1    Cosnard, M.Y.2
  • 13
    • 84976845336 scopus 로고
    • Testing unconstrained optimization software
    • Mar.
    • More, J. J., Garbow, B. S., and Hillstrom, K. E. Testing unconstrained optimization software. ACM Trans. Math. Softw. 7, 1 (Mar. 1981), 17–41.
    • (1981) ACM Trans. Math. Softw. , vol.7 , Issue.1 , pp. 17-41
    • More, J.J.1    Garbow, B.S.2    Hillstrom, K.E.3
  • 15
    • 0009617603 scopus 로고
    • A three-dimensional analogue to the method of bisections for solving nonlinear equations
    • Sikorski, K. A three-dimensional analogue to the method of bisections for solving nonlinear equations. Math. Comput. 33, 146 (1979), 722–738.
    • (1979) Math. Comput. , vol.33 , Issue.146 , pp. 722-738
    • Sikorski, K.1
  • 16
    • 0000268052 scopus 로고
    • Bisection is optimal
    • Sikorski, K. Bisection is optimal. Numer. Math. 40 (1982), 111–117.
    • (1982) Numer. Math. , vol.40 , pp. 111-117
    • Sikorski, K.1
  • 17
    • 0002123713 scopus 로고
    • Computing the topological degree of a mapping in Rn
    • Stenger, F. Computing the topological degree of a mapping in Rn. Numer. Math. 25 (1975), 23–38.
    • (1975) Numer. Math. , vol.25 , pp. 23-38
    • Stenger, F.1
  • 19
    • 84963178282 scopus 로고
    • An algorithm for numerical calculation of topological degree
    • Stynes, M. An algorithm for numerical calculation of topological degree. Appl. Anal. 9 (1979), 63–77.
    • (1979) Appl. Anal. , vol.9 , pp. 63-77
    • Stynes, M.1
  • 20
    • 0009648810 scopus 로고
    • A simplification of Stenger's topological degree formula
    • Stynes, M. A simplification of Stenger's topological degree formula. Numer. Math. 33 (1979), 147–156.
    • (1979) Numer. Math. , vol.33 , pp. 147-156
    • Stynes, M.1
  • 21
    • 0009648660 scopus 로고
    • On the construction of sufficient refinements for computation of topological degree
    • Stynes, M. On the construction of sufficient refinements for computation of topological degree. Numer. Math. 37 (1981), 453–462.
    • (1981) Numer. Math. , vol.37 , pp. 453-462
    • Stynes, M.1
  • 25
    • 0000669129 scopus 로고
    • An error estimation for the method of bisection in Rn
    • Vrahatis, M. N. An error estimation for the method of bisection in Rn. Bull. Greek Math. Soc. 27 (1986), 161–174.
    • (1986) Bull. Greek Math. Soc. , vol.27 , pp. 161-174
    • Vrahatis, M.N.1
  • 27
    • 0002592135 scopus 로고
    • A rapid generalized method of bisection for solving systems of non-linear equations
    • Vrahatis, M. N., and Iordanidis, K. I. A rapid generalized method of bisection for solving systems of non-linear equations. Numer. Math. 49 (1986), 123–138.
    • (1986) Numer. Math. , vol.49 , pp. 123-138
    • Vrahatis, M.N.1    Iordanidis, K.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.