On Bairstow’s method for the solution of polynomial equations
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- by Kenneth W. Brodlie PDF
- Math. Comp. 29 (1975), 816-826 Request permission
Abstract:
We show that Bairstow’s method is just one member of a family of similar algorithms for determining a quadratic factor of a polynomial. We suggest a way of choosing an appropriate member of this family for a particular problem. Numerical results indicate that our strategy compares favorably with the classical Bairstow algorithm.References
- Duane A. Adams, A stopping criterion for polynomial root finding, Comm. ACM 10 (1967), 655–658. MR 0240969, DOI 10.1145/363717.363775 D. W. ARTHUR, "Extension of Bairstow’s method for multiple quadratic factors," J. Inst. Math. Appl., v. 9, 1972, pp. 194-197. L. BAIRSTOW, Investigations Relating to the Stability of the Aeroplane, Reports and Memoranda #154, Advisory Committee for Aeronautics, October 1914, pp. 51-64. J. A. C. BINGHAM, "An improvement to iterative methods of polynomial factorization," Comm. ACM, v. 10, 1967, pp. 57-60.
- F. M. Carrano, A modified Bairstow method for multiple zeros of a polynomial, Math. Comp. 27 (1973), 781–792. MR 334492, DOI 10.1090/S0025-5718-1973-0334492-5
- Peter Henrici, Elements of numerical analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0166900
- P. Henrici and Bruce O. Watkins, Finding zeros of a polynomial by the $\textrm {Q-D}$ algorithm, Comm. ACM 8 (1965), 570–574. MR 0179935, DOI 10.1145/365559.365619
- Donald W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math. 11 (1963), 431–441. MR 153071, DOI 10.1137/0111030
- G. Peters and J. H. Wilkinson, Practical problems arising in the solution of polynomial equations, J. Inst. Math. Appl. 8 (1971), 16–35. MR 298931, DOI 10.1093/imamat/8.1.16
- Louis B. Rall, Computational solution of nonlinear operator equations, John Wiley & Sons, Inc., New York-London-Sydney, 1969. With an appendix by Ramon E. Moore. MR 0240944 R. F. THOMAS, "Corrections to numerical data on QD algorithm," Comm. ACM, v. 9, 1966, pp. 322-323.
- J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 816-826
- MSC: Primary 65H05
- DOI: https://doi.org/10.1090/S0025-5718-1975-0381283-7
- MathSciNet review: 0381283