Coconvex polynomial approximation

✍ Scribed by D. Leviatan; I.A. Shevchuk

• Book ID: 104142799
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 215 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(02)00045-x

✦ Synopsis

Let f AC½À1; 1 change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson-type estimates and summarize the positive and negative results in a truth-table as we have previously done for comonotone approximation.