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Jenkins, M.A. and Traub, J.F. (1970) A Three-Stage Variable-Shift Iteration for Polynomial Zeros and Its Relation to Generalized Rayleigh Iteration. Numerische Mathematik, 14, 252-263.
https://doi.org/10.1007/bf02163334

has been cited by the following article:

• TITLE: Method of Successive Polynomial Substitutions for Computing Roots of Polynomials

  AUTHORS: Serdar Beji

  KEYWORDS: Real and Complex Roots of Polynomials, Method of Successive Polynomial Substitutions, Accurate and Efficient Computation of Zeros of Polynomials

  JOURNAL NAME: Advances in Pure Mathematics, Vol.16 No.6, June 16, 2026

  ABSTRACT: A recursive technique, termed method of successive polynomial substitutions for computing all the real and complex roots of a polynomial of any given degree, is introduced. The method proceeds by reducing the degree of polynomial by one at each stage of successive polynomial substitutions; extracts a root, and continues until reaching a second-degree polynomial whose roots are obtained analytically. Coefficients of the polynomial may be real or complex; no initial guess is needed and the results are highly accurate. Sample computations for polynomials of various degrees and the code used in computations are given.