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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References | Similar Articles | Additional Information

**[1]**W. M. Kincaid,*A two-point method for the numerical solution of systems of simultaneous equations*, Quart, Appl. Math.**18**, 313-324 (1961) MR**0119411****[2]**A. M. Ostrowski,*Solutions of equations and systems of equations*, Academic Press, N. Y. (1960) MR**0216746****[3]**J. E. Dennis,*On the Kantorovich hypothesis for Newton's method*, SIAM J. Numer. Anal.**6**, 493-507 (1969)**[4]**W. Rheinboldt,*Symposium on the numerical solution of nonlinear problems*, Philadelphia, Pa., 1968**[5]**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) MR**0375068****[6]**E. Goursat,*A course in mathematical analysis*, V.**1**,*Applications to geometry, expansion in series, definite integrals derivatives and differentials*.**[7]**M. J. D. Powell,*A method for minimizing a sum of squares of nonlinear functions without calculating derivatives*, Computer J.**7**, 303-307 (1965) MR**0172456****[8]**F. Stenger,*Computing the topological degree of a mapping in n-space*, to appear in Numer. Math. MR**0394639****[9]**J. M. Ortega and W. C. Rheinboldt,*Iterative solutions of nonlinear equations in several variables*, Academic Press, New York (1970) MR**0273810****[10]**J. Mawhin,*Degré topologique et solutions périodiques des systèmes differentiels nonlinéaires*, Bull. Soc. Roy. Sciences de Liège**38**, 308-398 (1969) MR**0594965****[11]**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**[12]**J. L. Kuester and J. H. Mize,*Optimization techniques with Fortran*, McGraw-Hill, 1973, 368-386**[13]**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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DOI:
https://doi.org/10.1090/qam/455361

Article copyright:
© Copyright 1976
American Mathematical Society