The Numerical Stability of the Schur-Cohn Criterion

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Previous article Next article The Numerical Stability of the Schur-Cohn CriterionIrene GargantiniIrene Gargantinihttps://doi.org/10.1137/0708003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z., 14 (1922), 110–148 10.1007/BF01215894 MR1544543 CrossrefGoogle Scholar[2] I. Gargantini, Study of the rounding error in the complete Homer scheme, Internal Rep., Computer Science Dept., University of Western Ontario, London, to appear Google Scholar[3] Peter Henrici, Elements of numerical analysis, John Wiley & Sons Inc., New York, 1964xv+328 MR0166900 0149.10901 Google Scholar[4] Peter Henrici and , Irene Gargantini, B. Dejon and , P. Henrici, Uniformly convergent algorithms for the simultaneous approximation of all zeros of a polynomial, Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967), Wiley-Interscience, New York, 1969, 77–113 MR0256553 0194.46902 Google Scholar[5] D. H. Lehmer, A machine method for solving polynomial equations, J. Assoc. Comput. Mach., 8 (1961), 151–162 0106.10203 CrossrefGoogle Scholar[6] D. H. Lehmer, Search procedures for polynomial equation solving, Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967), Wiley-Interscience, New York, 1969, 193–208 MR0267750 0182.21503 Google Scholar[7] Morris Marden, Geometry of polynomials, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966xiii+243 MR0225972 0162.37101 Google Scholar[8] Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York, 1965xix+578 MR0191070 0139.31603 Google Scholar[9] I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math., 148 (1918), 122–145 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Geometry and dynamics of the Schur–Cohn stability algorithm for one variable polynomialsMathematics of Control, Signals, and Systems, Vol. 31, No. 4 | 5 September 2019 Cross Ref Bernoulli, Quotient-Difference, and Integral MethodsNumerical Methods for Roots of Polynomials - Part II | 1 Jan 2013 Cross Ref Height reducing property of polynomials and self-affine tilesGeometriae Dedicata, Vol. 152, No. 1 | 9 December 2010 Cross Ref Volume 8, Issue 1| 1971SIAM Journal on Numerical Analysis1-177 History Submitted:04 April 1968Published online:14 July 2006 InformationCopyright © 1971 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0708003Article page range:pp. 24-29ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics