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  Almost Tight Recursion Tree Bounds for the Descartes Method

Eigenwillig, A., Sharma, V., & Yap, C. K. (2006). Almost Tight Recursion Tree Bounds for the Descartes Method. In ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation (pp. 71-78). New York, USA: ACM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-21EB-9 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-21EC-7
Genre: Conference Paper

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ESY-DescTree-ISSAC06-authprep.pdf (Any fulltext), 184KB
 
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Copyright (c) ACM, 2006. This is the authors' version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in the Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation (ISSAC 2006), http://doi.acm.org/10.1145/1145768.1145786
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 Creators:
Eigenwillig, Arno1, Author           
Sharma, Vikram1, Author           
Yap, Chee K., Author
Dumas, Jean-Guillaume, Editor
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We give a unified ("basis free") framework for the Descartes method for real root isolation of square-free real polynomials. This framework encompasses the usual Descartes' rule of sign method for polynomials in the power basis as well as its analog in the Bernstein basis. We then give a new bound on the size of the recursion tree in the Descartes method for polynomials with real coefficients. Applied to polynomials $A(X) = \sum_{i=0}^n a_iX^i$ with integer coefficients $\abs{a_i} < 2^L$, this yields a bound of $O(n(L + \log n))$ on the size of recursion trees. We show that this bound is tight for $L = \Omega(\log n)$, and we use it to derive the best known bit complexity bound for the integer case.

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Language(s): eng - English
 Dates: 2007-04-272006
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314542
Other: Local-ID: C1256428004B93B8-6E09CB7FBE62EA64C12571B20040A5D4-Eigenwillig2006a
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Title: Untitled Event
Place of Event: Genova, Italy
Start-/End Date: 2006-07-09

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Title: ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Source Genre: Proceedings
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Publ. Info: New York, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 71 - 78 Identifier: ISBN: 1-59593-276-3