Abstract
Given a univariate polynomial over C, we discuss two issues, an algebraic method for separating a factor of mutually close roots from the polynomial, and a reasonable formula for the minimum root separation, by assuming that the close roots form well-separated clusters. The technique we use is very simple and effective; we move the origin near to the center of a close-root cluster, and then we are able to treat the other roots collectively, reducing the problem to a very simple one. Following this idea, we present a very simple and stable algebraic method for separating the close-root cluster, derive two lower-bound formulas for the distance between two close roots, and obtain a fairly simple lower bound of the minimum root separation of polynomials over C.
Work supported in part by the Japanese Ministry of Education, Science and Culture under Grants 15300002.
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Sasaki, T., Kako, F. (2007). An Algebraic Method for Separating Close-Root Clusters and the Minimum Root Separation. In: Wang, D., Zhi, L. (eds) Symbolic-Numeric Computation. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7984-1_10
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DOI: https://doi.org/10.1007/978-3-7643-7984-1_10
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