Abstract
An iteration method for roots of algebraic functions with roots of multiplicity greater than one is established using tools and techniques from interval arithmetic. The method is based on an interval iteration functions for multiple roots and it retains the convergence order of the underlying iteration method while preserving global convergence over an initial interval. A number of simple examples are provided to show that the method is feasible and that it produces reasonable results.
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Lin, Q., Rokne, J.G. An interval iteration for multiple roots of transcendental equations. Bit Numer Math 35, 561–571 (1995). https://doi.org/10.1007/BF01739827
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DOI: https://doi.org/10.1007/BF01739827