Best L2 local approximation Academic Article uri icon

abstract

  • In 1934, Walsh noted that the Taylor polynomial of degree n can be obtained by taking the limit as ε{lunate} → 0 + of the net of nth degree polynomials which best approximate f in the closed discs | z | ≤ ε{lunate}. Later, this result was generalized to rational approximation. In a recent paper, Shisha and the first two authors generalized this idea to the idea of best local approximation. In this paper, using a different technique, we study this problem in the L 2 setting. Consequently, better results follow under weaker hypotheses. © 1978.

author list (cited authors)

  • Chui, C. K., Smith, P. W., & Ward, J. D.

citation count

  • 10

publication date

  • March 1978