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Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials
dc.creator | Akritas, A. G. | en |
dc.date.accessioned | 2015-11-23T10:21:52Z | |
dc.date.available | 2015-11-23T10:21:52Z | |
dc.date.issued | 2009 | |
dc.identifier.issn | 0948-695X | |
dc.identifier.uri | http://hdl.handle.net/11615/25410 | |
dc.description.abstract | In this paper we review the existing linear and quadratic complexity (upper) bounds on the values of the positive roots of polynomials and their impact on the performance of the Vincent-Akritas-Strzebonski (VAS) continued fractions method for the isolation of real roots of polynomials. We first present the following four linear complexity bounds (two "old" and two "new" ones, respectively): Cauchy's, (C), Kioustelidis', (K), First-Lambda, (FL) and Local-Max, (LM); we then state the quadratic complexity extensions of these four bounds, namely: CQ, KQ, FLQ, and LMQ - the second, (KQ), having being presented by Hong back in 1998. All eight bounds are derived from Theorem 5 below. The estimates computed by the quadratic complexity bounds are less than or equal to those computed by their linear complexity counterparts. Moreover, it turns out that VAS(lmq) - the VAS method implementing LMQ - is 40% faster than the original version VAS(cauchy). | en |
dc.source | Journal of Universal Computer Science | en |
dc.source.uri | <Go to ISI>://WOS:000266699100003 | |
dc.subject | upper bounds | en |
dc.subject | positive roots | en |
dc.subject | real root isolation | en |
dc.subject | Vincent's theorem | en |
dc.subject | COMPUTING BOUNDS | en |
dc.subject | REAL ROOTS | en |
dc.subject | Computer Science, Software Engineering | en |
dc.subject | Computer Science, Theory & | en |
dc.subject | Methods | en |
dc.title | Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials | en |
dc.type | journalArticle | en |
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