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  New bounds for the Descartes method

Krandick, W., & Mehlhorn, K. (2006). New bounds for the Descartes method. Journal of Symbolic Computation, 41, 49-66.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2384-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2385-A
Genre: Journal Article

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Mehlhorn_a_2006_e.pdf (Any fulltext), 493KB
 
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 Creators:
Krandick, Werner1, Author           
Mehlhorn, Kurt1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We give a new bound for the number of recursive subdivisions in the Descartes method for polynomial real root isolation. Our proof uses Ostrowski’s theory of normal power series from 1950 which has so far been overlooked in the literature. We combine Ostrowski’s results with a theorem of Davenport from 1985 to obtain our bound. We also characterize normality of cubic polynomials by explicit conditions on their roots and derive a generalization of one of Ostrowski’s theorems.

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Language(s): eng - English
 Dates: 2007-04-262006
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: eDoc: 314367
Other: Local-ID: C1256428004B93B8-8291BD2AF8984049C12571C50041D379-mehlhorn06e
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Title: Journal of Symbolic Computation
Source Genre: Journal
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Pages: - Volume / Issue: 41 Sequence Number: - Start / End Page: 49 - 66 Identifier: -