About: Real-root isolation

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In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together, contain all the real roots of the polynomial.

Attributes	Values
rdfs:label	Aislamiento de raíces reales (es) Real-root isolation (en)
rdfs:comment	En matemáticas, y más específicamente en análisis numérico y cálculo simbólico, el aislamiento de raíces reales de un polinomio consiste en determinar un conjunto de intervalos disjuntos de la recta real, que contienen cada una (y solo una) raíz real del polinomio, y que conjuntamente contienen todas las raíces reales del polinomio. (es) In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together, contain all the real roots of the polynomial. (en)
foaf:depiction
dcterms:subject	Real algebraic geometry Polynomials Root-finding algorithms Computer algebra
Wikipage page ID	44012866 (xsd:integer)
Wikipage revision ID	1084890480 (xsd:integer)
Link from a Wikipage to another Wikipage	Root-finding algorithm Algorithm Real algebraic geometry Joseph-Louis Lagrange Descartes' rule of signs Numerical digit Worst-case complexity Sign variation Computer Computer algebra Continued fraction Convergent (continued fraction) Mathematics Nikola Obreshkov George E. Collins Möbius transformation Sturm's theorem Computational complexity Euclidean algorithm for polynomials Alexander Ostrowski Fibonacci number Mathematical analysis Floating-point Floating point Half-open interval Interval (mathematics) Interval arithmetic Polynomials Root-finding algorithms Computer algebra Wilkinson's polynomial VEB Deutscher Verlag der Wissenschaften Polynomial Polynomial greatest common divisor Square-free polynomial Budan's theorem Newton's method Rational number Root of a function Real line Properties of polynomial roots Yun's algorithm Translation (mathematics) James V. Uspensky Primitive part Soft O notation Complexity analysis Square-free factorization
Link from a Wikipage to an external page	http://www.lana.lt/journal/19/Akritas.pdf http://gallica.bnf.fr/ark:/12148/bpt6k57787134/f4.image.r=Agence%20Rol.langEN http://math-doc.ujf-grenoble.fr/JMPA/PDF/JMPA_1838_1_3_A19_0.pdf%7Cjournal=Journal http://www.lana.lt/journal/30/Akritas.pdf%7Cdoi=10.15388/NA.2008.13.3.14557 https://web.archive.org/web/20131029193332/http:/math-doc.ujf-grenoble.fr/JMPA/PDF/JMPA_1838_1_3_A19_0.pdf%7Carchive-date=2013-10-29%7Curl-status=dead https://web.archive.org/web/20140714222659/http:/retro.seals.ch/cntmng%3Ftype=pdf&rid=ensmat-001:1998:44::149&subp=hires%7Carchive-date=2014-07-14%7Curl-status=dead https://www.google.com/search%3Fq=uspensky+theory+of+equations&btnG=Search+Books http://dl.acm.org/citation.cfm%3Fid=32457 http://retro.seals.ch/cntmng%3Ftype=pdf&rid=ensmat-001:1998:44::149&subp=hires%7Cjournal=L'Enseignement http://sites.mathdoc.fr/JMPA/PDF/JMPA_1836_1_1_A28_0.pdf%7Cjournal=Journal
sameAs	Real-root isolation Real-root isolation Real-root isolation
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has abstract	En matemáticas, y más específicamente en análisis numérico y cálculo simbólico, el aislamiento de raíces reales de un polinomio consiste en determinar un conjunto de intervalos disjuntos de la recta real, que contienen cada una (y solo una) raíz real del polinomio, y que conjuntamente contienen todas las raíces reales del polinomio. (es) In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together, contain all the real roots of the polynomial. Real-root isolation is useful because usual root-finding algorithms for computing the real roots of a polynomial may produce some real roots, but, cannot generally certify having found all real roots. In particular, if such an algorithm does not find any root, one does not know whether it is because there is no real root. Some algorithms compute all complex roots, but, as there are generally much fewer real roots than complex roots, most of their computation time is generally spent for computing non-real roots (in the average, a polynomial of degree n has n complex roots, and only log n real roots; see Geometrical properties of polynomial roots § Real roots). Moreover, it may be difficult to distinguish the real roots from the non-real roots with small imaginary part (see the example of Wilkinson's polynomial in next section). The first complete real-root isolation algorithm results from Sturm's theorem (1829). However, when real-root-isolation algorithms began to be implemented on computers it appeared that algorithms derived from Sturm's theorem are less efficient than those derived from Descartes' rule of signs (1637). Since the beginning of 20th century there is an active research activity for improving the algorithms derived from Descartes' rule of signs, getting very efficient implementations, and computing their computational complexity. The best implementations can routinely isolate real roots of polynomials of degree more than 1,000. (en)
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page length (characters) of wiki page	32433 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Real-root_isolation
is Link from a Wikipage to another Wikipage of	Root-finding algorithms Bisection method Descartes' rule of signs Isolation Nikola Obreshkov Geometrical properties of polynomial roots Sturm's theorem Gröbner basis Jacques Charles François Sturm

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