A note on Chambers' method
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.
-  Ll. G. Chambers, A quadratic formula for finding the root of an equation, Math. Comp. 25 (1971), 305–307. MR 0295559, https://doi.org/10.1090/S0025-5718-1971-0295559-1
-  M. G. Cox, A note on Chambers’ method for finding a zero of a function, Math. Comp. 26 (1972), 749–750. MR 0327020, https://doi.org/10.1090/S0025-5718-1972-0327020-0
-  David M. Young and Robert Todd Gregory, A survey of numerical mathematics. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0408188
-  We are indebted to the referee for suggesting this final comparison.
- 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)
- 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)
- 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)
- 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