A note on Chambers’ method

Blackburn, J. A.; Beaudoin, Y.

doi:10.1090/S0025-5718-1974-0341850-2

Mathematics of Computation

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A note on Chambers’ method
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by J. A. Blackburn and Y. Beaudoin PDF

Math. Comp. 28 (1974), 573-574 Request permission

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

Ll. G. Chambers, A quadratic formula for finding the root of an equation, Math. Comp. 25 (1971), 305–307. MR 295559, DOI 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 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