Piecewise quadratic bounding functions for finding real roots of polynomials

Abstract

<p style='text-indent:20px;'>In this paper, our main interest is to create/ construct a new useful and outstanding algorithm to obtain roots of the real polynomial represented by <inline-formula><tex-math id="M1">\begin{document}$ f(x) = c_{0}+c_{1}x+...+c_{i}x^{i}+...+c_{n}x^{n} $\end{document}</tex-math></inline-formula> where coefficients of the polynomials are real numbers and <inline-formula><tex-math id="M2">\begin{document}$ x $\end{document}</tex-math></inline-formula> is a real number in the closed interval of <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} $\end{document}</tex-math></inline-formula>. Also, our results are supported by numerical examples. Then, a new algorithm is compared with the others (writer classical methods) and this algorithm is more useful than others.</p>