Abstract
In this paper, we extend the interval Newton method to the case where the interval derivative may contain zero. This extended method will isolate and bound all the real roots of a continuously differentiable function in a given interval. In particular, it will bound multiple roots. We prove that the method never fails to converge.
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References
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Hansen, E. A globally convergent interval method for computing and bounding real roots. BIT 18, 415–424 (1978). https://doi.org/10.1007/BF01932020
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DOI: https://doi.org/10.1007/BF01932020