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- W2150973910 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 per- formance of the Vincent-Akritas-Strzebonski (VAS) continued fractions method for the isolation of real roots of polynomials. We first present the following four linear complex- ity bounds (two old and two new ones, respectively): C auchy's, (C ), K ioustelidis', (K ), F irst-Lambda, (FL )a ndLocal-M ax, (LM ); we then state the quadratic complex- ity extensions of these four bounds, namely: CQ, KQ, FLQ ,a ndLMQ — 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) —t heVAS method implementing LMQ — is 40% faster than the original version VAS(cauchy)." @default.
- W2150973910 created "2016-06-24" @default.
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- W2150973910 date "2009-01-01" @default.
- W2150973910 modified "2023-09-23" @default.
- W2150973910 title "Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials" @default.
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