Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

The Degree of Piecewise Monotone Interpolation

Eli Passow and Louis Raymon
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 409-412
DOI: 10.2307/2040274
Stable URL: http://www.jstor.org/stable/2040274
Page Count: 4
  • Read Online (Free)
  • Download ($30.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Degree of Piecewise Monotone Interpolation
Preview not available

Abstract

Let $0 = x_0 < x_1 < \cdots < x_k = 1$ and let y0, y1, ⋯, yk be real numbers such that yj - 1 ≠ yj, j = 1, 2, ⋯, k. Estimates are obtained on the degree of an algebraic polynomial p(x) that interpolates the given data piecewise monotonely; i.e., such that (i) p(xj) = yj, j = 0, 1, ⋯, k, and such that (ii) p(x) is increasing on Ij = (xj - 1, xj) if $y_j < y_{j - 1}$, and decreasing on Ij if $y_j < y_{j - 1}, j = 1, 2, \cdots, k$. The problem is seen to be related to the problem of monotone approximation.

Page Thumbnails

  • Thumbnail: Page 
409
    409
  • Thumbnail: Page 
410
    410
  • Thumbnail: Page 
411
    411
  • Thumbnail: Page 
412
    412