FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034972350> ?p ?o ?g. }

• W2034972350 endingPage "298" @default.
• W2034972350 startingPage "292" @default.
• W2034972350 abstract "Isolation of the real roots of a polynomial equation is the process of finding real, disjoint intervals such that each contains exactly one real root and every real root is contained in some interval. This process is quite important because, as J. B. J. Fourier pointed out, it constitutes the first step toward the solution of general equations of degree greater than four, the second step being the approximation of roots to any desired degree of accuracy. In the beginning of the 19th century F. D. Budan and J. B. J. Fourier presented two different (but equivalent) theorems which enable us to determine the maximum possible number of real roots that an equation has within a given interval. Budan's theorem appeared in 1807 in the memoir Nouvelle methode pour la resolution des equations numeriques [10, p. 219], whereas Fourier's theorem was first published in 1820 in Le Bulletin des sciences par la Societe Philomatique de Paris, pp. 156, 181 [10, p. 223]. Due to the importance of these two theorems, there was a great controversy regarding priority rights. In his book (1859) Biographies of distinguished scientific men, p. 383, F. Arago informs us that Fourier deemed it necessary to have recourse to the certificates of early students of the Polytechnic School or Professors of the University in order to prove that he had taught his theorem in 1796, 1797 and 1803 [10]. Based on Fourier's proposition, C. Sturm presented in 1829 an improved theorem whose application yields the exact number of real roots which a polynomial equation without multiple zeros has within a real interval; thus he solved the real root isolation problem. Since 1830 Sturm's method has been the only one widely known and used, and consequently Budan's theorem was pushed into oblivion. To our knowledge, Budan's theorem can be found only in [16] and [61 whereas Fourier's proposition appears in almost all texts on the theory of equations. We feel that Budan's theorem merits special attention because it constitutes the basis of Vincent's forgotten theorem of 1836 which, in turn, is the foundation of our method for the isolation of the real roots of an equation [1], a method which far surpasses Sturm's in efficiency [2], [3]. In the discussion which follows we present separately, and without proofs, the classical theorems by Fourier and Budan and we indicate how they lead to the corresponding real root isolation methods. Some empirical results are also presented for comparison." @default.
• W2034972350 created "2016-06-24" @default.
• W2034972350 creator A5017435174 @default.
• W2034972350 date "1982-11-01" @default.
• W2034972350 modified "2023-09-27" @default.
• W2034972350 title "Reflections on a Pair of Theorems by Budan and Fourier" @default.
• W2034972350 cites W1970836040 @default.
• W2034972350 cites W1984091345 @default.
• W2034972350 cites W1994261260 @default.
• W2034972350 cites W2022919394 @default.
• W2034972350 cites W2035254827 @default.
• W2034972350 cites W2037111706 @default.
• W2034972350 cites W2102994533 @default.
• W2034972350 cites W413656932 @default.
• W2034972350 cites W4232927474 @default.
• W2034972350 cites W93715741 @default.
• W2034972350 doi "https://doi.org/10.1080/0025570x.1982.11977000" @default.
• W2034972350 hasPublicationYear "1982" @default.
• W2034972350 type Work @default.
• W2034972350 sameAs 2034972350 @default.
• W2034972350 citedByCount "8" @default.
• W2034972350 countsByYear W20349723502014 @default.
• W2034972350 countsByYear W20349723502017 @default.
• W2034972350 countsByYear W20349723502023 @default.
• W2034972350 crossrefType "journal-article" @default.
• W2034972350 hasAuthorship W2034972350A5017435174 @default.
• W2034972350 hasConcept C102519508 @default.
• W2034972350 hasConcept C114614502 @default.
• W2034972350 hasConcept C134306372 @default.
• W2034972350 hasConcept C202444582 @default.
• W2034972350 hasConcept C207864730 @default.
• W2034972350 hasConcept C33923547 @default.
• W2034972350 hasConceptScore W2034972350C102519508 @default.
• W2034972350 hasConceptScore W2034972350C114614502 @default.
• W2034972350 hasConceptScore W2034972350C134306372 @default.
• W2034972350 hasConceptScore W2034972350C202444582 @default.
• W2034972350 hasConceptScore W2034972350C207864730 @default.
• W2034972350 hasConceptScore W2034972350C33923547 @default.
• W2034972350 hasIssue "5" @default.
• W2034972350 hasLocation W20349723501 @default.
• W2034972350 hasOpenAccess W2034972350 @default.
• W2034972350 hasPrimaryLocation W20349723501 @default.
• W2034972350 hasRelatedWork W1978042415 @default.
• W2034972350 hasRelatedWork W2017331178 @default.
• W2034972350 hasRelatedWork W2060455831 @default.
• W2034972350 hasRelatedWork W2069016457 @default.
• W2034972350 hasRelatedWork W2305542682 @default.
• W2034972350 hasRelatedWork W2329001915 @default.
• W2034972350 hasRelatedWork W2976797620 @default.
• W2034972350 hasRelatedWork W3086542228 @default.
• W2034972350 hasRelatedWork W3106133691 @default.
• W2034972350 hasRelatedWork W4249580765 @default.
• W2034972350 hasVolume "55" @default.
• W2034972350 isParatext "false" @default.
• W2034972350 isRetracted "false" @default.
• W2034972350 magId "2034972350" @default.
• W2034972350 workType "article" @default.