@article{oai:ipsj.ixsq.nii.ac.jp:00012339,
 author = {Akira, Terui and Tateaki, Sasaki and Akira, Terui and Tateaki, Sasaki},
 issue = {4},
 journal = {情報処理学会論文誌},
 month = {Apr},
 note = {Let $P(x)$ be a given real univariate polynomial and let$?tilde{P}(x)=P(x)+?varDelta(x)$  where $?varDelta(x)$ is the sum oferror terms  that is  a polynomial with small real unknown but boundedcoefficients.  We first consider specifying the ``existence domain''of the values of $?tilde{P}(x)$  or the domain in which the value of$?tilde{P}(x)$ exists for any real number $x$  by the coefficientbounds for $?varDelta(x)$  and then introduce a concept of an``approximate real zero-point'' of $?tilde{P}(x)$.  We present apractical method for estimating the existence domain of zero-points of$?tilde{P}(x)$ by applying Smith's celebrated theorem.  We nextconsider counting the number of real zero-points of $?tilde{P}(x)$.If all the zero-points are sufficiently far apart from each other  thenumber of real zero-points of $?tilde{P}(x)$ is the same as that of$P(x)$  and we derive a condition for which we can assert that $P(x)$and $?tilde{P}(x)$ have the same number of real zero-points.  Wecalculate the actual number of real zero-points by Sturm's method which encounters the so-called small leading coefficient problem.  Forthis problem  we show that  under some conditions  small leading termscan be discarded.  Furthermore  we investigate four methods forevaluating the effect of error terms on the elements of the Sturmsequence., Let $P(x)$ be a given real univariate polynomial and let$\tilde{P}(x)=P(x)+\varDelta(x)$, where $\varDelta(x)$ is the sum oferror terms, that is, a polynomial with small real unknown but boundedcoefficients.  We first consider specifying the ``existence domain''of the values of $\tilde{P}(x)$, or the domain in which the value of$\tilde{P}(x)$ exists for any real number $x$, by the coefficientbounds for $\varDelta(x)$, and then introduce a concept of an``approximate real zero-point'' of $\tilde{P}(x)$.  We present apractical method for estimating the existence domain of zero-points of$\tilde{P}(x)$ by applying Smith's celebrated theorem.  We nextconsider counting the number of real zero-points of $\tilde{P}(x)$.If all the zero-points are sufficiently far apart from each other, thenumber of real zero-points of $\tilde{P}(x)$ is the same as that of$P(x)$, and we derive a condition for which we can assert that $P(x)$and $\tilde{P}(x)$ have the same number of real zero-points.  Wecalculate the actual number of real zero-points by Sturm's method,which encounters the so-called small leading coefficient problem.  Forthis problem, we show that, under some conditions, small leading termscan be discarded.  Furthermore, we investigate four methods forevaluating the effect of error terms on the elements of the Sturmsequence.},
 pages = {974--989},
 title = {Approximate Zero-points of Real Univariate Polynomial with Large Error Terms},
 volume = {41},
 year = {2000}
}