Approximation by GP box-splines on a four-direction mesh

• Published in: Journal of computational and applied mathematics Vol. 221; no. 2; pp. 310 - 329
• Main Authors: Conti, Costanza, Gori, Laura, Pitolli, Francesca, Sablonnière, Paul
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 15-11-2008; Elsevier
• Subjects: Approximation operators; Approximations and expansions; Box-splines; Exact sciences and technology; Mathematical analysis; Mathematics; Numerical Analysis; Numerical analysis. Scientific computation; Numerical approximation; Refinable functions; Sciences and techniques of general use; Box-splines; Approximation operators; Refinable functions; Numerical approximation; Integer; Scaling function; Numerical analysis; Grid pattern; Applied mathematics; Spline approximation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2007.10.036

On a four-directional uniform mesh of the plane, we define and study
C
0
Gori–Pitolli (abbreviated as GP) quadratics and
C
1
GP quartics generated by integer translates of GP box-splines generalizing respectively the classical
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1
quadratic box-spline and one of the
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2
quartic box-splines. More specifically, we study the approximation of a bivariate function
f
by some quasi-interpolants and interpolants with values in these generalized spline spaces.