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
A. M. Ostrowski,Solution of Equations and Systems of Equations, 2nd ed. (Academic Press, New York 1966) (Appendices A, B).
G. Polya undG. Szegö,Aufgaben und Lehrsätze der Analysis, Band 1, 3. Aufl. (Springer-Verlag, Berlin 1964).
W. Börsch-Supan,Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation, Numer. Math.14, 287 (1970).
B. T. Smith,Zero Sets for Polynomials and Computable Regions Containing These Sets, to appear.
M. Gutknecht andB. T. Smith,A Posteriori Error Bounds for the Zeros of a Polynomial, in preparation.
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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