Near minimally normed spline quasi-interpolants on uniform partitions

• Published in: Journal of computational and applied mathematics Vol. 181; no. 1; pp. 211 - 233
• Main Authors: Barrera, D., Ibáñez, M.J., Sablonnière, P., Sbibih, D.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2005; Elsevier
• Subjects: Approximations and expansions; B-splines; Discrete quasi-interpolants; Exact sciences and technology; Infinity norm; Integral quasi-interpolants; Mathematical analysis; Mathematics; Numerical Analysis; Numerical analysis. Scientific computation; Numerical approximation; Sciences and techniques of general use; Integral quasi-interpolants; Infinity norm; Discrete quasi-interpolants; B-splines; B spline; Discontinuity; Partition; Error estimation; Discrete data; Spline approximation; Numerical approximation; Interpolation; Upper bound; Numerical analysis; Applied mathematics; spline approximation; spline quasi-interpolants
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2004.11.031

Spline quasi-interpolants (QIs) are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline QIs on uniform partitions of the real line having small infinity norms. We call them near minimally normed QIs: they are exact on polynomial spaces and minimize a simple upper bound of their infinity norms. We give precise results for cubic and quintic QIs. Also the QI error is considered, as well as the advantage that these QIs present when approximating functions with isolated discontinuities.