On the type of a polynomial relative to a circle — An open problem

  • John J. H. Miller
Mathematical Programming And Numerical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 27)


This paper is a sequel to [2]. In it we prove a Theorem and Corollary which imply, in particular, the unproved Theorem 4 of that paper. In addition we analyze the reasons for the failure, in certain special cases, of an algebraic algorithm for determining the type of a polynomial relative to a circle. For background material the reader is referred in addition to [1], [3], [4] and the references contained in those papers.


  1. 1.
    JOHN J. H. MILLER, "On the location of zeros of certain classes of polynomials with applications to numerical analysis" J. Inst. Math. Applic. 8 (1971) 397–406.Google Scholar
  2. 2.
    JOHN J. H. MILLER, "On weak stability and the type of polynomial" Lecture Notes in Mathematics Vol. 228, Ed. John L1. Morris. Springer-Verlag (1971) 316–320.Google Scholar
  3. 3.
    JOHN J. H. MILLER, "Practical algorithms for finding the type of a polynomial". Studies in Numerical Analysis, Ed. B. K. P. Scaife. Academic Press (1974) 253–264.Google Scholar
  4. 4.
    D. P. MC CARTHY and JOHN J. H. MILLER, "The Refinement and Implementation of an algorithm for finding the type of a polynomial". Séminaires Analyse Numérique 1972–1973, J. L. Lions, P. A. Raviart Université Paris VI.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • John J. H. Miller
    • 1

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