Abstract
The behaviour of different iteration schemes, when used to find a high order zero, is studied from the point of view of function value reduction. It is found that the ratio between successive function values, for a given scheme, converges to a value for increasing order of the zero.
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References
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Gonnet, G.H. A short note on convergence near a high order zero. BIT 16, 338–339 (1976). https://doi.org/10.1007/BF01932277
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DOI: https://doi.org/10.1007/BF01932277