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Roots of polynomials: Durand-Kerner
  Finds the roots of a (real coefficients) polynomial by the method of Durand-Kerner.
2025.Feb.22 21:17:51
Coefficients Coeffs., c, of monic polynomial (see below). •
Mode   Mode: start from given roots or coefficients. •
tol • Tolerance (for iterations, etc.). •
Show steps ? Shows the intermediate steps.
  Finds the roots of a monic polynomial, p(x), with real coefficients, c, such that p(x) = Σ ci xn−i = c0 xn + c1 xn−1 + ... + cn−1 x + cn, c0 = 1, by the method of Durand and Kerner (no multiple or pure imaginary roots).

(Not implemented) If the roots are given, the coefficients of the polynomial are calculated beforehand, to permit checking.

The basis data lead to x = (2.587, 0.206±1.375i).
  Suggested alternative data, with results: c = ( -3 3 -5 -1 3), x = (2.58, 0.75, -0.655, 0.163±1.532i)

References: Plate: DurandKerner

• Durand, Émile, 1960, "Solutions numériques des équations algébriques", Masson (1961, tome II).

• Kerner, I. O., 1966, Numer. Math., 18, pp 290–294.

• 1877-02-14: Landau, Edmund Georg Hermann (1938-02-19).

 
 
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Created: 2010-02-14 — Last modified: 2016-12-23