A Relation Between Newton’s Method and Successive Approximations for Quadratic Irrationals

Julian Palmore

Chapter 25 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 254-258 from Springer

Abstract: Abstract A quadratic irrational, 1 ζ, has the form (a + b 1/2)/c, where a, b, c are integers, b > 0, b is not the square of an integer, and c ≠ 0. Let ζ+ and ζ− be quadratic irrationals corresponding to ζ+ = (a + b 1/2)/c and ζ− (a − b 1/2)/c. A quadratic polynomial that has these roots is p(z) = (z − ζ+)(z − ζ−), or $$p(z) = z^2 - \frac{{2a}} {c}z + \frac{{a^2 - b}} {{c^2 }}$$

Keywords: Successive Approximation; Global Attractor; Convergent Sequence; Dynamical System Theory; Linear Fractional Transformation (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_25

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DOI: 10.1007/978-1-4612-2740-3_25

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