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Newton's method and the Jenkins-Traub algorithm

Author: R. N. Pederson
Journal: Proc. Amer. Math. Soc. 97 (1986), 687-690
MSC: Primary 30C15
MathSciNet review: 845988
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Abstract: In this paper we propose to show how a multi-increment version of Newton's method can be used to obtain starting points for the Jenkins-Traub algorithm.

References [Enhancements On Off] (What's this?)

  • [1] M. A. Jenkins, Three-stage variable-shift iterations for the solution of polynomial equations with a posteriori error bounds for the zeros, Dissertation, Stanford Univ., Stanford, Calif., 1969. Available as Rep. CS 138, Computer Science Department, Stanford Univ.
  • [2] M. A. Jenkins and J. F. Traub, A three-stage variable shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numer. Math. 14 (1970), 252-261. MR 0258271 (41:2918)
  • [3] J. F. Traub, A class of globally convergent iteration functions for the solution of polynomial equations, Math. Comp. 20 (1966), 113-138. MR 0192655 (33:880)
  • [4] -, Proof of global convergence of an iterative method for calculating complex zeros of a polynomial, Notices Amer. Math. Soc. 13 (1966), 117.
  • [5] -, The calculation of zeros of polynomials and analytic functions, Mathematical Aspects of Computer Science, Proc. Sympos. Appl. Math., vol. 19, Amer. Math. Soc., Providence, R.I., 1967, pp. 138-152. Also available as Rep. CS 36, Computer Science Department, Stanford Univ., Stanford, Calif., 1966. MR 0233965 (38:2286)
  • [6] M. A. Jenkins and J. F. Traub, A three stage algorithm for real polynomials using quadratic iteration, Siam J. Numer. Anal. 7 (1970). MR 0279995 (43:5716)

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