Summary
The errors of the approximations to the zeros of a polynomial are analyzed, supposing these approximations have been found successively using factorization of the polynomial. We deduce an error bound depending only of the degree of the polynomial and the values of the reduced polynomials at the approximation being factored. The same method may be used to calculate error bounds in the case where round-off is involved.
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Literatur
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Für zahlreiche Diskussionen und Verbesserungen bin ich den Herren Prof. Dr. P. Henrici und dipl. Math. Rolf Jeltsch zu Dank verpflichtet.
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Gutknecht, M. A priori Fehlerschranken für sukzessiv abgespaltene Polynomnullstellen. Journal of Applied Mathematics and Physics (ZAMP) 22, 630–634 (1971). https://doi.org/10.1007/BF01614005
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DOI: https://doi.org/10.1007/BF01614005