Abstract
In this paper, interval arithmetic using an underlying multiple precision arithmetic is briefly presented. Then interval Newton iteration for solving nonlinear equations is introduced. A new Newton's algorithm based on multiple precision interval arithmetic is given, along with its properties: termination, arbitrary accuracy on the computed zeros, automatic and dynamic adaptation of the precision. Finally, some experiments illustrate the behaviour of this method.
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Revol, N. Interval Newton Iteration in Multiple Precision for the Univariate Case. Numerical Algorithms 34, 417–426 (2003). https://doi.org/10.1023/B:NUMA.0000005354.92791.41
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DOI: https://doi.org/10.1023/B:NUMA.0000005354.92791.41