Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems

Journal of the ACM (JACM)

Volumn 17, Issue 4, 1970, Pages 661-674

  Smith, Brian T ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

06A; JACOA; MATHEMATICS; POLYNOMIALS;

EID: 0014855549     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/321607.321615     Document Type: Article

References (13)

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3. Birkoff, George D. An elementary double inequality for the roots of an algebraic equation having greatest absolute value. Bull. Amer. Math. Soc. 21 (1916), 494-495.
4. Burnside, W. S., and Panton, A. W. The Theory of Equations. Longmans, Green and Co., London, 1886, pp. 297-298.
5. Daniels, J. W. Correcting approximations to multiple roots of polynomials. Numer. Math. 9 (1966), 99-102.
6. Henrici, P., AND Watkins, B. O. Finding zeros of a polynomial by the Q-D algorithm. Comm. ACM 8, 9 (Sept. 1965), 570-574.
7. Marden, M. Geometry of Zeros. Amer. Math. Soc., Providence, R. I., 1966.
8. Smith, B. T. Zerpol, a zero finding algorithm for polynomials using Laguerre's method. Proc. 1967 Army Numerical Analysis Conference, Madison, Wis., May 1967 (Rep. 67-3, US Army Res. Office—Durham, Durham, N. C., Nov. 1967), pp. 153-174.
9. Smith, B. T. Zerpol. Error bounds, based upon Gerschgorin's theorems, for the zeros of a polynomial. Tech. Rep. 9, Dep. of Computer Sci., U. of Toronto, Toronto, Ontario, July 1969 (Ph.D. thesis).
10. Spitzbart, A. A generalization of Hermite's interpolation formula. Amer. Math. Mon. 67 (1960), 42-46.
11. Staff, Institute Of Computer Science, University Of Toronto. Programmer's Reference Manual for the IBM 7094-II Computer, 2nd ed., Vol. II. University of Toronto, Toronto, Ontario, 1968.
12. Taussky, O., AND Marcus, M. Eigenvalues of finite matrices. InTodd, J., Ed., A Survey of Numerical Analysis, McGraw-Hill, New York, 1962, pp. 279-313.
13. Thomas, R. F., JR. Corrections to numerical data on Q-D algorithm. Letter to Editor, Comm. ACM 9, 5 (May 1966), 322-323.