Abstract
On some Properties of an Interval Newton Type Method and its Modification. Considered is an interval iterative Newton type method for enclosing a real simple root of the nonlinear equation f(x) = 0 in a given interval X. The method has a simple formulation in terms of extended interval arithmetic. Cubic convergence of the method is proved assuming that f possesses a Lipschitzian second derivative which vanishes at the root of the equation. A modification of the method with higher order of convergence is proposed. An algorithm with result verification is formulated and some numerical experiments are reported.
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Dedicated to Professor U. Kulisch on the occasion of his 60th birthday
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© 1993 Springer-Verlag
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Dimitrova, N.S. (1993). On Some Properties of an Interval Newton Type Method and its Modification. In: Albrecht, R., Alefeld, G., Stetter, H.J. (eds) Validation Numerics. Computing Supplementum, vol 9. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6918-6_3
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DOI: https://doi.org/10.1007/978-3-7091-6918-6_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82451-1
Online ISBN: 978-3-7091-6918-6
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