Principles for Testing Polynomial Zerofinding Programs

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Principles for Testing Polynomial Zerofinding Programs

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 1 , Issue 1 (March 1975) table of contents

Pages: 26 - 34

Year of Publication: 1975

ISSN:0098-3500

Authors

M. A. Jenkins	Department of Computing and Information Science, Queen's University, Kingston, Ont., Canada
J. F. Traub	Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 11, Downloads (12 Months): 44, Citation Count: 6

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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	Duane A. Adams, A stopping criterion for polynomial root finding, Communications of the ACM, v.10 n.10, p.655-658, Oct. 1967 [doi>10.1145/363717.363775]
	2	John A. C. Bingham, An improvement to iterative methods of polynomial factorization, Communications of the ACM, v.10 n.1, p.57-60, Jan. 1967 [doi>10.1145/363018.363063]
	3	BUSINGER, P.A. Private communication, 1969.
	4	CHAMPAGNe, W. P. On finding roots of polynomials by hook or by crook. Interim Tech. ep. 3, U. of Texas Computation Cent., Austin, Tex., 1964.
	5	CODL W.J. Software for the elementary functions, in Mathematical Software, J. R. Rice, Ed., Academic Press, New York., 1971, pp. 171-186.
	6	DEJON~ B., AND HENRICI, P., Eds. Constructive Aspects of the Fundamental Theorem of Algebra. Wfley-Interscience, New York, 1969.
	7	DUNAWAY, D. K. Calculation of zeros of a real polynomial through factorization using Euclid's algorithm. SIAM J. Numer. Anal. 11, 6 (Dec. 1974), 1087-1104.
	8	JENKINS, M.A. Three-stage variable-shift iterations for the solution of polynomiul equations with a posterlori error bounds for the zeros. Ph D. Diss., Stanford U., Stanford, Calif., 1969.
	9	JENKINS, M. A., AND TRAUB, J. F. A three-stage variable-shift iteration for polynomial zeros and Its relation to generahzed Rayleigh iteration. Numer. Math. 14 (1970), 252--263.
	10	JENKINS, M. A., AND TRAUB, j. F. A three-stage algorithm for real polynomials using quadratic iteration, SIAM J. Numer. Anal. 7 (1970), 545-566.
	11	JENKINS, M:. A., AND TRAUB, J. F. Principles for testing polynomial zerofinding programs. Proc. Mathematical Software II, Purdue U., West Lafayette, Ind., May 29-31, 1974, pp. 84-107. Also Tech. Rep., Dep. of Computer Sci., Carnegie-Mellon U., Pittsburgh, Pa., March 1974.
	12	KAHAN, W. Numerical analysis lectures. Stanford, Calif., 1966.
	13	PETERS, G., AND WILKINSON, J.H. Practical problems arising in the solution of polynomial equations. J. Inst. Math. Appl. 8 (1971), 16-35.
	14	SMIrk, B. T. A zerofinding algorithm using Laguerre's method. M.Sc. Th., U. of Toronto, Toronto, Ont., Canada, 1967.
	15	Brian T. Smith, Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems, Journal of the ACM (JACM), v.17 n.4, p.661-674, Oct. 1970 [doi>10.1145/321607.321615]
	16	James H. Wilkinson, Rounding Errors in Algebraic Processes, Dover Publications, Incorporated, 1994

CITED BY 6

	Herbert S. Wilf, A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane, Journal of the ACM (JACM), v.25 n.3, p.415-420, July 1978
	S. Schmidt , J. A. Brown , M. A. Jenkins, Eigenanalysis and polynomial root finding primitive functions, ACM SIGAPL APL Quote Quad, v.13 n.1, p.320-324, September 1982
	T. E. Hull , R. Mathon, The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence, ACM Transactions on Mathematical Software (TOMS), v.22 n.3, p.261-280, Sept. 1996
	M. A. Jenkins, Algorithm 493: Zeros of a Real Polynomial [C2], ACM Transactions on Mathematical Software (TOMS), v.1 n.2, p.178-189, June 1975
	J. R. Rice , C. W. Gear , J. Ortega , B. Parlett , M. Schultz , L. F. Shampine , P. Wolfe , J. F. Traub, Numerical computations: its nature and research directions, ACM SIGNUM Newsletter, v.14 n.si-1, p.1-48, February 1979
	Zhonggang Zeng, Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities, ACM Transactions on Mathematical Software (TOMS), v.30 n.2, p.218-236, June 2004