Algorithm 666: Chabis: a mathematical software package for locating and evaluating roots of systems of nonlinear equations

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Algorithm 666: Chabis: a mathematical software package for locating and evaluating roots of systems of nonlinear equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 14 , Issue 4 (December 1988) table of contents

Pages: 330 - 336

Year of Publication: 1988

ISSN:0098-3500

Author

Michael N. Vrahatis

Cornell Univ., Ithaca, NY

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 2, Downloads (12 Months): 31, Citation Count: 5

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appendices and supplements abstract references cited by index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

CHABIS (666.gz) (11 KB)

characteristic bisection.: locating and evaluating roots of systems of nonlinear equations
Gams: F2

ABSTRACT

CHABIS is a mathematical software package for the numerical solution of a system of n nonlinear equations in n variables. First, CHABIS locates at least one solution of the system within an n-dimensional polyhedron. Then, it applies a new generalized method of bisection to this n-polyhedron in order to obtain an approximate solution of the system according to a predetermined accuracy. In this paper we briefly describe the user interface to CHABIS and present several details of its implementation, as well as an example of its usage.

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	AMERICAN NATIONAL STANDARDS INSTITUTE. ANSI FORTRAN X3.9-1978. ANSI, New York, 1978. (Also known as FORTRAN 77.)
	2	Jack J. Dongarra , Jeremy Du Croz , Sven Hammarling , Richard J. Hanson, An extended set of FORTRAN basic linear algebra subprograms, ACM Transactions on Mathematical Software (TOMS), v.14 n.1, p.1-17, March 1988 [doi>10.1145/42288.42291]
	3	Jack J. Dongarra , Jeremy Du Croz , Sven Hammarling , Richard J. Hanson, Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs, ACM Transactions on Mathematical Software (TOMS), v.14 n.1, p.18-32, March 1988 [doi>10.1145/42288.42292]
	4	R. J. Hanson , F. T. Krogh, ALGORITHM 653: translation of algorithm 539: PC-BLAS, basic linear algebra subprograms for FORTRAN usage with the INTEL 8087, 80287 numeric data processor, ACM Transactions on Mathematical Software (TOMS), v.13 n.3, p.311-317, Sept. 1987 [doi>10.1145/29380.214346]
	5	C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
	6	C. L. Lawson , R. J. Hanson , F. T. Krogh , D. R. Kincaid, Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1], ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.324-325, Sept. 1979 [doi>10.1145/355841.355848]
	7	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 [doi>10.1145/50063.214384]

CITED BY 5

	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
	M. N. Vrahatis , G. D. Magoulas , V. P. Plagianakos, From linear to nonlinear iterative methods, Applied Numerical Mathematics, v.45 n.1, p.59-77, April 2003
	B. Boutsinas , M. N. Vrahatis, Artificial nonmonotonic neural networks, Artificial Intelligence, v.132 n.1, p.1-38, October 2001
	A. D. Anastasiadis , G. D. Magoulas , M. N. Vrahatis, Sign-based learning schemes for pattern classification, Pattern Recognition Letters, v.26 n.12, p.1926-1936, September 2005
	E. N. Malihoutsaki , I. A. Nikas , T. N. Grapsa, Improved Newton's method without direct function evaluations, Journal of Computational and Applied Mathematics, v.227 n.1, p.206-212, May, 2009