In this paper odd-order B-spline filters are proposed to reconstruct volumetric data sampled on an optimal Body-Centered Cubic (BCC) grid. To make these filters nearly interpolating, we adapt a previously published framework, which is based on a discrete frequency-domain prefiltering. It is shown that a BCC-sampled B-spline kernel is not invertible, therefore the interpolation constraint cannot...

In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our theoretical findings.

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

The collocation methods based on cubic B-spline, are developed to approximate solution of the second and first kind Fredholm integral equations.First we collocate the solution by B-spline and the Newton-Cotes formula is used to approximate integral. Convergence analysis has been investigated and proved that the quadratur rule is fourth order convergent. The presented methods are tested to the p...

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

On Schwarz's domain decomposition methods for elliptic boundary value problems, submitted for publication, 1996. 6. M. J. Lai and P. Wenston, Bivariate spline method for numerical solution of steady state Navier-Stokes equations over polygons in stream function formulation, submitted, 1997. Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in

S For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothi...

Recently there has been an increasing interest in exploiting computational and statistical techniques for the purpose of component analysis of indirect calorimetry data. Using these methods it becomes possible to dissect daily energy expenditure into its components and to assess the dynamic response of the resting metabolic rate (RMR) to nutritional and pharmacological manipulations. To perform...

This article considers testing the hypothesis of Generalized Linear Models (GLM) versus general smoothing spline models for data from exponential families. The tests developed are based on the connection between smoothing spline models and Bayesian models (Gu (1992)). They are extensions of the locally most powerful (LMP) test of Cox, Koh, Wahba and Yandell (1988), the generalized maximum likel...

Quadratic Spline Collocation Methods for Systems of Elliptic PDEs Kit Sun Ng Master of Science Graduate Department of Computer Science University of Toronto 2000 We consider Quadratic Spline Collocation (QSC) methods for solving systems of two linear second-order PDEs in two dimensions. Optimal order approximation to the solution is obtained, in the sense that the convergence order of the QSC a...