In this paper, we first recall the definition of a family of Koenig’s rootfinding algorithms known as Koenig’s algorithms (𝐾,) for polynomials. In the whole paper p has degree 𝑑 ≥ 2 with real coefficients and real (and simple) zeros 𝑥 , 1 ≤ 𝑘 ≤ 𝑑 . Now we want to discuss Koenig’s algorithms in details where 𝑛 = 4, (𝐾,(𝑧)).
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