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.
- Ll. G. Chambers, A quadratic formula for finding the root of an equation, Math. Comp. 25 (1971), 305–307. MR 295559, DOI 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 327020, DOI 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.
M. G. Cox, "A note on Chambers’ method for finding a zero of a function," Math. Comp., v. 26, 1972, p. 749.
D. M. Young & R. T. Gregory, A Survey of Numerical Mathematics, Vol. I, Addison-Wesley, Reading, Mass., 1972, pp. 150-153.
We are indebted to the referee for suggesting this final comparison.
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