Newton’s method and the Jenkins-Traub algorithm
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- by R. N. Pederson PDF
- Proc. Amer. Math. Soc. 97 (1986), 687-690 Request permission
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
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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.
- 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 (1969/70), 252–263. MR 258271, DOI 10.1007/BF02163334
- J. F. Traub, A class of globally convergent iteration functions for the solution of polynomial equations, Math. Comp. 20 (1966), 113–138. MR 192655, DOI 10.1090/S0025-5718-1966-0192655-2 —, Proof of global convergence of an iterative method for calculating complex zeros of a polynomial, Notices Amer. Math. Soc. 13 (1966), 117.
- J. F. Traub, The calculation of zeros of polynomials and analytic functions, Proc. Sympos. Appl. Math., Vol. XIX, Amer. Math. Soc., Providence, R.I., 1967, pp. 138–152. MR 0233965
- M. A. Jenkins and J. F. Traub, A three-stage algorithm for real polynomials using quadratic iteration, SIAM J. Numer. Anal. 7 (1970), 545–566. MR 279995, DOI 10.1137/0707045
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 687-690
- MSC: Primary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1986-0845988-2
- MathSciNet review: 845988