Abstract
Suppose that some zeros of a (complex) polynomial are known to lie in specified circular regions. Then there are given algorithms to determine the remaining zeros with simultaneous computation of error bounds. The algorithms are based upon a modified Newton's method, their theoretical foundation and their application make use of circular arithmetic, an extension of interval arithmetic to the complex plane. The algorithms were constructed with special regard to multiple zeros and clusters of zeros. With suitable starting-approximations an approximation can be found iteratively together with an error bound for each zero.
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Literatur
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© 1975 Springer-Verlag Berlin Heidelberg
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Glatz, G. (1975). Newton-Algorithmen zur Bestimmung von Polynomwurzeln unter Verwendung komplexer Kreisarithmetik. In: Nickel, K. (eds) Interval Mathematics. IMath 1975. Lecture Notes in Computer Science, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07170-9_19
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DOI: https://doi.org/10.1007/3-540-07170-9_19
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