Interpolation at critical points of an algebraic polynomial: A review of a result due to C. Davis Articles uri icon

publication date

  • January 2018

start page

  • 31

end page

  • 49

issue

  • 1-2

volume

  • 25

International Standard Serial Number (ISSN)

  • 1315-4125

abstract

  • We consider an old problem on interpolation at critical points of
    an algebraic polynomial due to Chandler Davis. We essentially reproduce the
    proof given by this author in [C. Davis, 4714: Proposed solution: Problem
    4653, Amer. Math. Monthly 64(9) 729-730 (1957)]. We provide a detailed
    account of Davis' proof, adding some details that, in our opinion, make it
    even easier to follow. Some illustrative examples are also given.

subjects

  • Mathematics

keywords

  • interpolation, algebraic polynomials, critical points, chebyshev-bojanov; polynomials.