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Euler-like method for the simultaneous inclusion of polynomial zeros with Weierstass' correction

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Petkovic_232554.pdf
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2001

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Petkovic, Miodrag S.
Vranic, Dejan V.

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KRÄMER, Walter, ed. and others. Scientific computing, validated numerics, interval methods : [Proceedings of SCAN 2000 - The 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, and Interval 2000 - The International Conference on Interval Methods in Science and Engineering]. New York: Kluwer, 2001, pp. 153-164. ISBN 0-306-46706-2

Zusammenfassung

An improved iterative method of Euler's type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of fourth order, Carstensen-Petkovi c's approach [7]using Weierstrass' correction is applied. It is proved that the R-order of convergence of the improved Euler-like method is (asymptotically)2 + V7 = 4.646 or 5, depending of the type of applied inversion of a disk. The proposed algorithm possesses great computational e ciency since the increase of the convergence rate is obtained without additional calculations. Initial conditions which provide the guaranteed convergence of the considered method are also studied. These conditions are
computationally veri able, which is of practical importance.

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Scientific computing, validated numerics, interval methods, 19. Sept. 2000 - 22. Sept. 2000, Karlsruhe, Germany
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ISO 690PETKOVIC, Miodrag S., Dejan V. VRANIC, 2001. Euler-like method for the simultaneous inclusion of polynomial zeros with Weierstass' correction. Scientific computing, validated numerics, interval methods. Karlsruhe, Germany, 19. Sept. 2000 - 22. Sept. 2000. In: KRÄMER, Walter, ed. and others. Scientific computing, validated numerics, interval methods : [Proceedings of SCAN 2000 - The 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, and Interval 2000 - The International Conference on Interval Methods in Science and Engineering]. New York: Kluwer, 2001, pp. 153-164. ISBN 0-306-46706-2
BibTex
@inproceedings{Petkovic2001Euler-23255,
  year={2001},
  title={Euler-like method for the simultaneous inclusion of polynomial zeros with Weierstass' correction},
  isbn={0-306-46706-2},
  publisher={Kluwer},
  address={New York},
  booktitle={Scientific computing, validated numerics, interval methods : [Proceedings of SCAN 2000 - The 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, and Interval 2000 - The International Conference on Interval Methods in Science and Engineering]},
  pages={153--164},
  editor={Krämer, Walter},
  author={Petkovic, Miodrag S. and Vranic, Dejan V.}
}
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