In the work, we rebuild the masks of well-known interpolatory symmetric subdivision schemes-binary 2n-point interpolatory schemes, the ternary 4-point interpolatory scheme using only the symmetry and the necessary condition for smoothness and the butterfly scheme, and the modified butterfly scheme using the factorization property. 2006 Elsevier Inc. All rights reserved.

ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...

In this paper we derive an approximation property of four-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ...

The present paper provides a new definition of the dual interpolation curve in geometric-intuitive way based on adaptive refinement techniques. is an implementation interpolatory subdivision scheme for modeling, which comprises polynomial segments different degrees. Dual curves maintain various desirable properties conventional modeling methods, such as local subdivision, high accuracy and conv...

Several problems of mathematical physics lead to Fredholm integral equations of the second kind where the kernels are either weakly or strongly singular and the known terms are smooth. These equations have solutions which are smooth in the whole interval of integration except at the endpoints where they have mild singularities. In this paper we derive new pointwise and uniform polynomial approx...

In this study, we are concerned with non-stationary interpolatory subdivision schemes with refinement rules which may vary from level to level. First, we derive a new class of interpolatory non-stationary subdivision schemes reproducing exponential polynomials. Next, we prove that non-stationary schemes based on the known butterfly-shaped stencils possess the same smoothness as the known Butter...

In this paper we derive an approximation property of 4-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth ord...

In this sequel to [15, 16] we focus on the efficient solution of the linear block-systems arising from a Galerkin discretization of an elliptic partial differential equation of second order with the partition of unity method (PUM). We present a cheap multilevel solver for partition of unity discretizations of any order. The shape functions of a PUM are products of piecewise rational partition o...

BACKGROUND Our hypothesis that multiple, equally tensioned strands of hamstring graft used for reconstruction of the anterior cruciate ligament are stronger and stiffer than ten-millimeter patellar ligament grafts was tested biomechanically with use of tendons from cadavera. METHODS In the first part of the study, we measured the strength and stiffness of one, two, and four-strand hamstring g...