A modified Bairstow method for multiple zeros of a polynomial
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- by F. M. Carrano PDF
- Math. Comp. 27 (1973), 781-792 Request permission
Abstract:
A modification of Bairstow’s method to find multiple quadratic factors of a polynomial is presented. The nonlinear system of equations of the Bairstow method is replaced by high order partial derivatives of that system. The partials are computed by a repetition of the Bairstow recursion formulas. Numerical results demonstrate that the modified method converges in many cases where the Bairstow method fails due to the multiplicity of the quadratic factor. Rall [4] has described a generalization of Newton’s method for simultaneous nonlinear equations with multiple roots. This may be applied to solve the nonlinear Bairstow equations; however, it fails in some cases due to near-zero divisors. Examples are presented which illustrate the behavior of the author’s algorithm as well as the methods of Rall and Bairstow.References
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L. Bairstow, Investigations Relating to the Stability of the Aeroplane, Reports and Memoranda #154, Advisory Committee for Aeronautics, October 1914, pp. 51-64.
F. M. Carrano, A Generalized Bairstow Method for Multiple Zeros of a Polynomial, Ph.D. Dissertation, Syracuse University, Syracuse, N.Y., 1969.
- Peter Henrici, Elements of numerical analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0166900
- L. B. Rall, Convergence of the Newton process to multiple solutions, Numer. Math. 9 (1966), 23–37. MR 210316, DOI 10.1007/BF02165226
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 781-792
- MSC: Primary 65H05
- DOI: https://doi.org/10.1090/S0025-5718-1973-0334492-5
- MathSciNet review: 0334492