In this paper, we construct a bijective mapping between biquadratic spline space over the hierarchical T-mesh and piecewise constant corresponding crossing-vertex-relationship graph (CVR graph). We propose novel structure, by which offer an effective easy operative method for constructing basis functions of space. The is isomorphism. hold properties such as linear independence, completeness pro...

Battle-Lemarié’s wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to `. The passing and stopping bands of the ideal filter are depende...

draft jul74, T E Xed 1997 Carl de Boor 1. Specialization to the knot sequence Z 2. Cardinal spline interpolation 3. The exponential splines 4. Cardinal spline interpolation as the degree goes to infinity 5. Approximation of cardinal type 6. Semicardinal

draft jul74, T E Xed 1997 Carl de Boor 1. Specialization to the knot sequence Z 2. Cardinal spline interpolation 3. The exponential splines 4. Cardinal spline interpolation as the degree goes to infinity 5. Approximation of cardinal type 6. Semicardinal

Abstract Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different with orders of interpolation are normally used the various fields in order to avoid spurious oscillations. When including discontinuities these meshes, there exist several options discretisation. Herein we will discuss two which use T-splines, one aiming at minimum numb...

T-spline overcomes the topological constraints of the control net of NURBS model successfully. However, the introduction of T-junctions, L-junctions and the isolated vertices in the T-mesh makes its topological structure very flexible. As a result, not only the T-mesh is hard to be represented, but the computation and local refinement of T-spline are difficult to be implemented as well. This hi...

We construct bootstrap conndence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap conndence intervals are considered and compared. We nd that the commonly used bootstrap percentile intervals are inferior to the T intervals and to...

In this paper,wedesign differentiable, two-dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L(R). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box sp...