A note on Chambers' method

Authors:
J. A. Blackburn and Y. Beaudoin

Journal:
Math. Comp. **28** (1974), 573-574

MSC:
Primary 65H05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341850-2

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.

**[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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341850-2

Keywords:
Numerical analysis,
approximation to the root of an equation

Article copyright:
© Copyright 1974
American Mathematical Society