Splines with Minimal Defect and Decomposition Matrices

A. A. Makarov

Abstract


Finite-dimensional space of twice continuously differentiable splines on a nonuniform grid are considered. We also construct a system of linear functionals biorthogonal to the splines and resolve an interpolation problem generated by this system. We derive the decomposition matrices on an interval and on a segment for the space of forth order (third degree) splines associated with infinite and finite nonuniform grids respectively.

Keywords


Spline; Wavelet; Biorthogonal system; Decomposition matrix; Reconstruction matrix; Knot insertion; Refinement equation; Subdivision scheme

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v3i3.218

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