Algorithm to Construct Integro Splines

Abstract

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines $S_{m+1}(x)$ of neighbouring degrees to the given spline $S_m(x)$ with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.

C2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values

“…The authors in [21,34] provided some integro spline schemes for the case of non-polynomial splines. More recent work on the integro spline approximation is given in [35,36] In this work, a new class of integro spline approximant is introduced. The proposed operator is C 2 smooth everywhere and exactly reproduces both linear polynomials and hyperbolic functions, which is useful to avoid undesirable oscillations in curves' interpolation.…”