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On 04/26/2012 05:04 PM, Nate Hayes wrote:
the midpoint Interval Newton algorithm is undefined at Level 1 on input from unbounded interval.
This is true only for a particular version of the interval Newton algorithm that requires the evaluation at the midpoint, which is not dfefined for an unbounded interval. This just means that this particular version of the algorithm is ill-specified for the unbounded case.
However, any efficient interval Newton algorithm will allow evaluation at any point of the interval as a center, and not choosing the midpoint (if it exists) is in fact often superior to blindly using the midpoint as the center.
Arnold Neumaier