Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

In this article, a fourth order quintic spline method has been developed to obtain numerical solutions for second order boundary value problems with Dirichlet boundary conditions. The developments of the quintic spline method and convergence analysis were presented. Three test problems have been considered for comparison purposes. The numerical results showed that the quintic spline method is m...

In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clari cation and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline int...

the arya and paris model is a commonly accepted method to translate a particle-size distribution curve into a corresponding soil moisture characteristic curve using scaling parameter (α). the scaling parameter, in the original model of arya and paris (1981), was assumed constant (α=1.38) for all soil texture classes. in recent years, several studies have shown that α is not constant and its qua...

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...