Abstract
We derive upper and lower bounds for the positive roots of certain sequences of polynomials which arise in the determination of theR-order of iterative numerical processes.
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References
J. Herzberger,On the R-order of some recurrences with applications to inclusion methods, Computing 36, 175–180 (1986).
J. Herzberger,Über die Konvergenzordnungen einiger Klassen intervallmäßiger Iterationsverfahren, Z. Angew. Math. u. Mech. 66 (to appear).
J. W. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
A. Ostrowski,Solution of Equations and Systems of Equations, Academic Press, New York, 1960.
J. W. Schmidt,On the R-order of coupled sequences, Computing 26, 333–342 (1981).
Leonhard Thornheim,Convergence of multipoint iterative methods, J. ACM 11, 210–220 (1964).
J. F. Traub,Iterative Methods for the Solution of Equations, Prentice-Hall Inc., Englewood Cliffs, 1964.
R. Brent, Sh. Winograd and Ph. Wolfe,Optimal iterative processes for root-finding, Numer. Math. 20, 327–341 (1973).
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Herzberger, J. Bounds for theR-order of certain iterative numerical processes. BIT 26, 259–262 (1986). https://doi.org/10.1007/BF01933753
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DOI: https://doi.org/10.1007/BF01933753