On Bairstow's method for the solution of polynomial equations
Author:
Kenneth W. Brodlie
Journal:
Math. Comp. 29 (1975), 816826
MSC:
Primary 65H05
MathSciNet review:
0381283
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Abstract 
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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.
 [1]
Duane
A. Adams, A stopping criterion for polynomial root finding,
Comm. ACM 10 (1967), 655–658. MR 0240969
(39 #2314)
 [2]
D. W. ARTHUR, "Extension of Bairstow's method for multiple quadratic factors," J. Inst. Math. Appl., v. 9, 1972, pp. 194197.
 [3]
L. BAIRSTOW, Investigations Relating to the Stability of the Aeroplane, Reports and Memoranda #154, Advisory Committee for Aeronautics, October 1914, pp. 5164.
 [4]
J. A. C. BINGHAM, "An improvement to iterative methods of polynomial factorization," Comm. ACM, v. 10, 1967, pp. 5760.
 [5]
F.
M. Carrano, A modified Bairstow method for
multiple zeros of a polynomial, Math. Comp.
27 (1973),
781–792. MR 0334492
(48 #12811), http://dx.doi.org/10.1090/S00255718197303344925
 [6]
Peter
Henrici, Elements of numerical analysis, John Wiley & Sons
Inc., New York, 1964. MR 0166900
(29 #4173)
 [7]
P.
Henrici and Bruce
O. Watkins, Finding zeros of a polynomial by the
𝑄𝐷 algorithm, Comm. ACM 8 (1965),
570–574. MR 0179935
(31 #4172)
 [8]
Donald
W. Marquardt, An algorithm for leastsquares estimation of
nonlinear parameters, J. Soc. Indust. Appl. Math. 11
(1963), 431–441. MR 0153071
(27 #3040)
 [9]
G.
Peters and J.
H. Wilkinson, Practical problems arising in the solution of
polynomial equations, J. Inst. Math. Appl. 8 (1971),
16–35. MR
0298931 (45 #7980)
 [10]
Louis
B. Rall, Computational solution of nonlinear operator
equations, With an appendix by Ramon E. Moore, John Wiley & Sons
Inc., New York, 1969. MR 0240944
(39 #2289)
 [11]
R. F. THOMAS, "Corrections to numerical data on QD algorithm," Comm. ACM, v. 9, 1966, pp. 322323.
 [12]
J.
H. Wilkinson, Rounding errors in algebraic processes,
PrenticeHall Inc., Englewood Cliffs, N.J., 1963. MR 0161456
(28 #4661)
 [1]
 D. A. ADAMS, "A stopping criterion for polynomial rootfinding," Comm. ACM, v. 10, 1967, pp. 655658. MR 39 #2314. MR 0240969 (39:2314)
 [2]
 D. W. ARTHUR, "Extension of Bairstow's method for multiple quadratic factors," J. Inst. Math. Appl., v. 9, 1972, pp. 194197.
 [3]
 L. BAIRSTOW, Investigations Relating to the Stability of the Aeroplane, Reports and Memoranda #154, Advisory Committee for Aeronautics, October 1914, pp. 5164.
 [4]
 J. A. C. BINGHAM, "An improvement to iterative methods of polynomial factorization," Comm. ACM, v. 10, 1967, pp. 5760.
 [5]
 F. M. CARRANO, "A modified Bairstow method for multiple zeros of a polynomial," Math. Comp., v. 27, 1973, pp. 781792. MR 0334492 (48:12811)
 [6]
 P. HENRICI, Elements of Numerical Analysis, Wiley, New York, 1964. MR 29 # 4173. MR 0166900 (29:4173)
 [7]
 P. HENRICI & B. O. WATKINS, "Finding zeros of a polynomial by the QD algorithm," Comm. ACM, v. 8, 1965, pp. 570574. MR 31 #4172. MR 0179935 (31:4172)
 [8]
 D. W. MARQUARDT, "An algorithm for leastsquares estimation of nonlinear parameters," J. Soc. Indust. Appl. Math., v. 11, 1963, pp. 431441. MR 27 #3040. MR 0153071 (27:3040)
 [9]
 G. PETERS & J. H. WILKINSON, "Practical problems arising in the solution of polynomial equations," J. Inst. Math. Appl., v. 8, 1971, pp. 1635. MR 45 #7980. MR 0298931 (45:7980)
 [10]
 L. B. RALL, Computational Solution of Nonlinear Operator Equations, Wiley, New York, 1969. MR 39 #2289. MR 0240944 (39:2289)
 [11]
 R. F. THOMAS, "Corrections to numerical data on QD algorithm," Comm. ACM, v. 9, 1966, pp. 322323.
 [12]
 J. H. WILKINSON, Rounding Errors in Algebraic Processes, PrenticeHall, Englewood Cliffs, N. J., 1963. MR 28 #4661. MR 0161456 (28:4661)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197503812837
PII:
S 00255718(1975)03812837
Keywords:
Solution of polynomial equations,
Bairstow's method,
quadratic factors of a polynomial
Article copyright:
© Copyright 1975 American Mathematical Society
