A bisection method for systems of nonlinear equations

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A bisection method for systems of nonlinear equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 10 , Issue 4 (December 1984) table of contents

Pages: 367 - 377

Year of Publication: 1984

ISSN:0098-3500

Authors

A. Eiger	Rensselaer Polytechnic Institute, Rensselaer, NY
K. Sikorski	Columbia Univ., New York, NY
F. Stenger	Univ. of Utah, Salt Lake City, UT

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 17, Downloads (12 Months): 146, Citation Count: 7

Additional Information:

references cited by index terms review collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ALLGOWER, E.L., AND GEORG, K. Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations. SIAM Rev. 5, 22 (1980), 22-85.
	2	BOULT, T., AND SIKORSKI, K. Can we approximate zeros of functions with non-zero topological degree. Tech. Rep. Dept. of Computer Science, Columbia Univ., New York, 1984.
	3	EAVES, B.C. Homotopies for Computation of Fixed Points. SIAM Rev 3, 1 (1972), 1-22.
	4	EAVES, B.C. A Short Course in Solving Equations with PL Homotopies. In SIAM-AMS Proceedings (SIAM) 9, 1976, 73-143.
	5	EAVES, B.C., GOULD, F.J., PEITGEN, H.O., AND TODD, M.J., EDS. Homotopy Methods and Global Convergence Plenum, New York, 1983.
	6	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.
	7	KEARFOTT, B. AnEfficient Degree-Computation Method for a Generalized Method of Bisection. Numer. Math. 32 (1979), 109-127.
	8	Ralph Baker Kearfott, Computing the degree of maps and a generalized method of bisection., 1977
	9	KEARFOTT, B. An Improved Program for Generalized Bisection. To be published.
	10	James M. Ortega , Werner C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000
	11	PROFER, M., AND SIEGBERG, H.W. On Computational Aspects of Topological Degree in R n. Sonderforschungesbereich 72, Approximation und Optimierung, Preprint 257. Univ. Bonn, West Germany.
	12	SIKORSKI, K. A Three-Dimensional Analogue to the Method of Bisections for Solving Nonlinear Equations. Math. Comput. 33, 146 (1979), 722-738.
	13	SIKORSKI, K. Bisection is Optimal. Numer. Math. 40 (1982), 111-117.
	14	SIKORSKI, K., AND TROJAN, G.M. Asymptotic Optimality of the Bisection Method. Rep. Dept. of Computer Science, Columbia Univ., New York, 1984.
	15	STENGER, F. Computing the Topological Degree of a Mapping in R". Numer. Math. 25 (1975) 23-38.
	16	Martin Joseph Stynes, An algorithm for the numerical calculation of the degree of a mapping., 1977
	17	STYNES, M. A Simplification of Stenger's Topological Degree Formula. Numer. Math. 33 (1979), 147-156.
	18	STYNES, M. On the Construction of Sufficient Refinements for Computation of Topological Degree. Numer. Math 37 (1981), 453-462.
	19	TODD, M.J. The Computatwn of Fixed Points and Applications. Springer Lecture Notes in Economics and Mathematmal Systems, 124. Springer-Verlag, New York, 1976.
	20	TRAUB, J.F., AND WOZNIAKOWSKI, H. A General Theory of Optimal Algorithrns. Academic Press, New York, 1980.
	21	VAN DER LAAN, G., AND TALMAN, J.J. A Restart Algorithm for Completing Fixed Points without an Extra Dimension. Math. Program. 17 (1979), 74-84.
	22	VAN DER LAAN, G., AND TALMAN, J.J. A Class of Simplicial Restart Fixed Point Algorithms without an Extra Dimension. Math. Program. 20 (1981), 33-48.

CITED BY 7

	Monica Bianchini , Stefano Fanelli , Marco Gori, Optimal Algorithms for Well-Conditioned Nonlinear Systems of Equations, IEEE Transactions on Computers, v.50 n.7, p.689-698, July 2001
	Gabriel Taubin, Distance approximations for rasterizing implicit curves, ACM Transactions on Graphics (TOG), v.13 n.1, p.3-42, Jan. 1994
	R. Baker Kearfott, Some tests of generalized bisection, ACM Transactions on Mathematical Software (TOMS), v.13 n.3, p.197-220, Sept. 1987
	Michael N. Vrahatis, Solving systems of nonlinear equations using the nonzero value of the topological degree, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.312-329, Dec. 1988
	Alexander Morgan , Vadim Shapiro, Box-bisection for solving second-degree systems and the problem of clustering, ACM Transactions on Mathematical Software (TOMS), v.13 n.2, p.152-167, June 1987
	B. Mourrain , M. N. Vrahatis , J. C. Yakoubsohn, On the complexity of isolating real roots and computing with certainty the topological degree, Journal of Complexity, v.18 n.2, p.612-640, June 2002
	Iddo Hanniel , Gershon Elber, Subdivision termination criteria in subdivision multivariate solvers using dual hyperplanes representations, Computer-Aided Design, v.39 n.5, p.369-378, May, 2007

INDEX TERMS

Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.5 Roots of Nonlinear Equations
Subjects: Systems of equations

General Terms:
Algorithms, Performance, Theory

REVIEW

"Eldon R. Hansen : Reviewer"

The authors of this paper describe an algorithm for the solution of a system of nonlinear equations. The method is based on computation of the topological degree of a mapping and a simplex bisection scheme. The algorithm is globally convergent.< more...

Collaborative Colleagues:

A. Eiger: colleagues

K. Sikorski: colleagues

F. Stenger: colleagues

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