On near-best discrete quasi-interpolation on a four-directional mesh

✍ Scribed by D. Barrera; M.J. Ibáñez; P. Sablonnière; D. Sbibih

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 538 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.02.063

✦ Synopsis

Spline quasi-interpolants are practical and effective approximation operators. In this paper, we construct QIs with optimal approximation orders and small infinity norms called nearbest discrete quasi-interpolants which are based on Ω-splines, i.e. B-splines with octagonal supports on the uniform four-directional mesh of the plane. These quasi-interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters. We show that this problem has always a solution, in general nonunique. Concrete examples of such quasi-interpolants are given in the last section.