Abstract
Making use of the theory of continuous homotopy and the relation between symmetric polynomial and polynomial in one variable the authors devoted this article to constructing a regularly homotopic curve with probability one. Discrete tracing along this homotopic curve leads to a class of Durand-Kerner algorithm with step parameters. The convergence of this class of algorithms is given, which solves the conjecture about the global property of Durand-Kerner algorithm. The problem for steplength selection is thoroughly discussed. Finally, sufficient numerical examples are used to verify our theory.
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Communicated by Tang Renji
Project supported by the National Natural Science Foundation of China
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Deren, W., Fengguang, Z. The globalization of Durand-Kerner algorithm. Appl Math Mech 18, 1045–1057 (1997). https://doi.org/10.1007/BF00132798
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DOI: https://doi.org/10.1007/BF00132798