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Locating real multiple zeros of a real interval polynomial

Published: 09 July 2006 Publication History

Abstract

For a real interval polynomial F, we provide a rigorous method for deciding whether there exists a polynomial in F that has a multiple zero in a prescribed interval in R. We show that it is sufficient to examine a finite number of edge polynomials in F. An edge polynomial is a real interval polynomial such that the number of coefficients that are intervals is one. The decision method uses the property that a univariate polynomial is of degree one with respect to each coefficient regarded as a variable. Using this method, we can completely determine the set of real numbers each of which is a multiple zero of some polynomial in F.

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cover image ACM Conferences
ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation
July 2006
374 pages
ISBN:1595932763
DOI:10.1145/1145768
  • General Chair:
  • Barry Trager
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 09 July 2006

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Author Tags

  1. convex set
  2. interval polynomial
  3. real multiple zero

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  • (2019)The nearest complex polynomial with a zero in a given complex domainTheoretical Computer Science10.1016/j.tcs.2011.09.016412:50(7029-7043)Online publication date: 5-Jan-2019
  • (2019)Computing the nearest polynomial with a zero in a given domain by using piecewise rational functionsJournal of Symbolic Computation10.1016/j.jsc.2011.08.01246:12(1318-1335)Online publication date: 3-Jan-2019
  • (2009)On real factors of real interval polynomialsJournal of Symbolic Computation10.1016/j.jsc.2008.04.01444:7(908-922)Online publication date: 1-Jul-2009
  • (2008)The nearest polynomial with a zero in a given domain from a geometrical viewpointProceedings of the twenty-first international symposium on Symbolic and algebraic computation10.1145/1390768.1390808(287-294)Online publication date: 20-Jul-2008
  • (2008)The nearest polynomial with a zero in a given domainTheoretical Computer Science10.1016/j.tcs.2008.09.006409:2(282-291)Online publication date: 10-Dec-2008
  • (2008)The Nearest Real Polynomial with a Real Multiple Zero in a Given Real IntervalComputer Mathematics10.1007/978-3-540-87827-8_3(32-41)Online publication date: 2008
  • (2007)On real factors of real interval polynomialsProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277593(331-338)Online publication date: 29-Jul-2007
  • (2007)The nearest polynomial with a zero in a given domainProceedings of the 2007 international workshop on Symbolic-numeric computation10.1145/1277500.1277527(190-196)Online publication date: 25-Jul-2007

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