Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operato...

In this thesis, we propose to analyze panel count data using a spline-based sieve generalized estimating equation method with a semiparametric proportional mean model E(N(t)|Z) = Λ0 (t) e T 0 Z . The natural log of the baseline mean function, logΛ0 (t), is approximated by a monotone cubic B-spline function. The estimates of regression parameters and spline coefficients are the roots of the spli...

Multivariate refinable Hermite interpolants with high smoothness and small support are of interest in CAGD and numerical algorithms. In this article, we are particularly interested in analyzing some univariate and bivariate symmetric refinable Hermite interpolants, which have some desirable properties such as short support, optimal smoothness and spline property. We shall study the projection m...

Abstract In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of response, at any domain point, depends on full trajectory predictor. The AdaSS is obtained by optimization objective function with two spatially penalties, based initial estimates partial derivatives coefficient function. This allows proposed...

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We develop a rational biquadratic G analogue of the non-uniform C B-spline paradigm. These G splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, and combine them into one smoothly-connected structure. This enables a design process that starts with basic shapes, re-pepresents them in spline form and uses the spline form to provide shape handles for locali...

This paper discusses the dimension of spline spaces S(m,n,m−1, n−1,T ) over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space S(m,n,m− 1, n− 1,T ) and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory...

This paper presents a spline approximation method for the representation of a large set of points. The representation should be smooth with preserving important shape characteristics given by the points. Because of a large size of the set, the standard spline interpolation cannot be used. The proposed method is based on a least squares minimization of the distances of the points from the spline...