A two-dimensional analogue to the method of bisections for solving nonlinear equations
Authors:
Charles Harvey and Frank Stenger
Journal:
Quart. Appl. Math. 33 (1976), 351-368
MSC:
Primary 65H10
DOI:
https://doi.org/10.1090/qam/455361
MathSciNet review:
455361
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Additional Information
- W. M. Kincaid, A two-point method for the numerical solution of systems of simultaneous equations, Quart. Appl. Math. 18 (1960/61), 313–324. MR 119411, DOI https://doi.org/10.1090/S0033-569X-1961-0119411-4
- A. M. Ostrowski, Solution of equations and systems of equations, 2nd ed., Pure and Applied Mathematics, Vol. 9, Academic Press, New York-London, 1966. MR 0216746
J. E. Dennis, On the Kantorovich hypothesis for Newton’s method, SIAM J. Numer. Anal. 6, 493–507 (1969)
W. Rheinboldt, Symposium on the numerical solution of nonlinear problems, Philadelphia, Pa., 1968
- Ivo G. Rosenberg and Frank Stenger, A lower bound on the angles of triangles constructed by bisecting the longest side, Math. Comp. 29 (1975), 390–395. MR 375068, DOI https://doi.org/10.1090/S0025-5718-1975-0375068-5
E. Goursat, A course in mathematical analysis, V. 1, Applications to geometry, expansion in series, definite integrals derivatives and differentials.
- M. J. D. Powell, A method for minimizing a sum of squares of non-linear functions without calculating derivatives, Comput. J. 7 (1965), 303–307. MR 172456, DOI https://doi.org/10.1093/comjnl/7.4.303
- Frank Stenger, Computing the topological degree of a mapping in ${\bf R}^{n}$, Numer. Math. 25 (1975/76), no. 1, 23–38. MR 394639, DOI https://doi.org/10.1007/BF01419526
- J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
- Jean Mawhin, Degré topologique et solutions périodiques des systèmes différentiels non linéaires, Bull. Soc. Roy. Sci. Liège 38 (1969), 308–398 (French). MR 594965
A. Eiger and F. Stenger, A program of bisections for solving two nonlinear equations, University of Utah, Department of Mathematics, to appear in Comm. ACM
J. L. Kuester and J. H. Mize, Optimization techniques with Fortran, McGraw-Hill, 1973, 368–386
D. A. Paviani, A new method for the solution of a general nonlinear programming problem, Ph. D. dissertation, The University of Texas, 1968
W. M. Kincaid, A two-point method for the numerical solution of systems of simultaneous equations, Quart, Appl. Math. 18, 313–324 (1961)
A. M. Ostrowski, Solutions of equations and systems of equations, Academic Press, N. Y. (1960)
J. E. Dennis, On the Kantorovich hypothesis for Newton’s method, SIAM J. Numer. Anal. 6, 493–507 (1969)
W. Rheinboldt, Symposium on the numerical solution of nonlinear problems, Philadelphia, Pa., 1968
I. Rosenberg and F. Stenger, A lower bound on the angles of triangles constructed by bisecting the longest side, Math. Comp. 29, 390–395 (1975)
E. Goursat, A course in mathematical analysis, V. 1, Applications to geometry, expansion in series, definite integrals derivatives and differentials.
M. J. D. Powell, A method for minimizing a sum of squares of nonlinear functions without calculating derivatives, Computer J. 7, 303–307 (1965)
F. Stenger, Computing the topological degree of a mapping in n-space, to appear in Numer. Math.
J. M. Ortega and W. C. Rheinboldt, Iterative solutions of nonlinear equations in several variables, Academic Press, New York (1970)
J. Mawhin, Degré topologique et solutions périodiques des systèmes differentiels nonlinéaires, Bull. Soc. Roy. Sciences de Liège 38, 308–398 (1969)
A. Eiger and F. Stenger, A program of bisections for solving two nonlinear equations, University of Utah, Department of Mathematics, to appear in Comm. ACM
J. L. Kuester and J. H. Mize, Optimization techniques with Fortran, McGraw-Hill, 1973, 368–386
D. A. Paviani, A new method for the solution of a general nonlinear programming problem, Ph. D. dissertation, The University of Texas, 1968
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Article copyright:
© Copyright 1976
American Mathematical Society
