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Serdica J. Computing 2 (2008), 145162 FLQ, THE FASTEST QUADRATIC COMPLEXITY BOUND
 

Summary: Serdica J. Computing 2 (2008), 145­162
FLQ, THE FASTEST QUADRATIC COMPLEXITY BOUND
ON THE VALUES OF POSITIVE ROOTS OF POLYNOMIALS
Alkiviadis G. Akritas, Andreas I. Argyris, Adam W. StrzeboŽnski
On the 20th Anniversary of the University of Thessaly
Abstract. In this paper we present FLQ, a quadratic complexity bound on
the values of the positive roots of polynomials. This bound is an extension
of FirstLambda, the corresponding linear complexity bound and, conse-
quently, it is derived from Theorem 3 below. We have implemented FLQ
in the Vincent-Akritas-StrzeboŽnski Continued Fractions method (VAS-CF)
for the isolation of real roots of polynomials and compared its behavior with
that of the theoretically proven best bound, LMQ. Experimental results
indicate that whereas FLQ runs on average faster (or quite faster) than
LMQ, nonetheless the quality of the bounds computed by both is about the
same; moreover, it was revealed that when VAS-CF is run on our benchmark
polynomials using FLQ, LMQ and min(FLQ, LMQ) all three versions run
equally well and, hence, it is inconclusive which one should be used in the
VAS-CF method.
ACM Computing Classification System (1998): G.1.5, F.2.1, I.1.2.
Key words: Vincent's theorem, real root isolation methods, linear and qua-dratic complexity

  

Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly

 

Collections: Computer Technologies and Information Sciences