On Bairstow's method for the solution of polynomial equations

Author:
Kenneth W. Brodlie

Journal:
Math. Comp. **29** (1975), 816-826

MSC:
Primary 65H05

MathSciNet review:
0381283

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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****[2]**D. W. ARTHUR, "Extension of Bairstow's method for multiple quadratic factors,"*J. Inst. Math. Appl.*, v. 9, 1972, pp. 194-197.**[3]**L. BAIRSTOW,*Investigations Relating to the Stability of the Aeroplane*, Reports and Memoranda #154, Advisory Committee for Aeronautics, October 1914, pp. 51-64.**[4]**J. A. C. BINGHAM, "An improvement to iterative methods of polynomial factorization,"*Comm. ACM*, v. 10, 1967, pp. 57-60.**[5]**F. M. Carrano,*A modified Bairstow method for multiple zeros of a polynomial*, Math. Comp.**27**(1973), 781–792. MR**0334492**, 10.1090/S0025-5718-1973-0334492-5**[6]**Peter Henrici,*Elements of numerical analysis*, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR**0166900****[7]**P. Henrici and Bruce O. Watkins,*Finding zeros of a polynomial by the 𝑄-𝐷 algorithm*, Comm. ACM**8**(1965), 570–574. MR**0179935****[8]**Donald W. Marquardt,*An algorithm for least-squares estimation of nonlinear parameters*, J. Soc. Indust. Appl. Math.**11**(1963), 431–441. MR**0153071****[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****[10]**Louis B. Rall,*Computational solution of nonlinear operator equations*, With an appendix by Ramon E. Moore, John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR**0240944****[11]**R. F. THOMAS, "Corrections to numerical data on QD algorithm,"*Comm. ACM*, v. 9, 1966, pp. 322-323.**[12]**J. H. Wilkinson,*Rounding errors in algebraic processes*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR**0161456**

Retrieve articles in *Mathematics of Computation*
with MSC:
65H05

Retrieve articles in all journals with MSC: 65H05

Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1975-0381283-7

Keywords:
Solution of polynomial equations,
Bairstow's method,
quadratic factors of a polynomial

Article copyright:
© Copyright 1975
American Mathematical Society