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Halley rule


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1: 9.17 Methods of Computation
Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule3.8(ii)) or Halley’s rule3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations. …
2: 10.74 Methods of Computation
Newton’s rule3.8(i)) or Halley’s rule3.8(v)) can be used to compute to arbitrarily high accuracy the real or complex zeros of all the functions treated in this chapter. …Newton’s rule is quadratically convergent and Halley’s rule is cubically convergent. …
3: 3.8 Nonlinear Equations
Another iterative method is Halley’s rule: …