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A note on Chambers' method

Authors: J. A. Blackburn and Y. Beaudoin
Journal: Math. Comp. 28 (1974), 573-574
MSC: Primary 65H05
MathSciNet review: 0341850
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Abstract: A correction is given for one of Chambers' second-order iteration formulae. It is shown that composition of the secant method with itself exhibits a convergence exponent of 2.414, whereas composition of the iteration function with itself yields an exponent of 2.831.

References [Enhancements On Off] (What's this?)

  • [1] Ll. G. Chambers, "A quadratic formula for finding the root of an equation," Math. Comp., v. 25, 1971, pp. 305-307. MR 45 #4625. MR 0295559 (45:4625)
  • [2] M. G. Cox, "A note on Chambers' method for finding a zero of a function," Math. Comp., v. 26, 1972, p. 749. MR 0327020 (48:5362)
  • [3] D. M. Young & R. T. Gregory, A Survey of Numerical Mathematics, Vol. I, Addison-Wesley, Reading, Mass., 1972, pp. 150-153. MR 0408188 (53:11954a)
  • [4] We are indebted to the referee for suggesting this final comparison.

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Keywords: Numerical analysis, approximation to the root of an equation
Article copyright: © Copyright 1974 American Mathematical Society

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