• DocumentCode
    808136
  • Title

    Zeros of f(z) = (az-b)npm (cz-d)n

  • Author

    Oraizi, Homayoon

  • Author_Institution
    Syracuse University, Syracuse, NY, USA
  • Volume
    17
  • Issue
    2
  • fYear
    1972
  • fDate
    4/1/1972 12:00:00 AM
  • Firstpage
    259
  • Lastpage
    261
  • Abstract
    The zeros of f(z) = (az - b)^{n} \\pm (cz - d)^{n} are found to lie on a circle of radius |(ad - cb)/(|a|^{2} - |c|^{2})| with its center at z = (a^{\\ast }b - c^{\\ast }d)/(|a|^{2} - |c|^{2}) , where a, b, c , and d are complex numbers and n is assumed real. When |a| = |c| the locus of the zeros is a straight line perpendicular to the line joining the points b/a and b/c and intersecting it at z = 0.5(b/a + d/c) . The zeros are found analytically and constructed geometrically.
  • Keywords
    Polynomials; Convergence; Eigenvalues and eigenfunctions; Multidimensional systems; Newton method; Polynomials; Riccati equations;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1972.1099926
  • Filename
    1099926
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=808136