We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces, which are composed of a hierarchy of nested spaces. The hierarchical quasi-interpolants are described in terms of the truncated hierarchical basis. Once for each level in the hierarchy a quasi-interpolant is selected in the corresponding space, the hierarchical quasi-interpolants are obtained witho...

This paper is concerned with the description of an algorithm for generating the B-nets of box splines and an algorithm based on subdivision of these B-nets for graphically displaying spline surfaces on a three-or four-directional mesh. The combination of these two algorithms is shown to compare favorably over the other existing algorithms for this purpose. 0 1 x1. Introduction It is well known ...

In this paper, a modified orthogonal linear spline (OL-spline) is used for the numerical solution of coupled nonlinear inverse reaction-diffusion problem to determine unknown boundary conditions. The convergence properties new combination are obtained. A quasi-linearization technique utilized linearize term in equations. This process produces system equations which can be solved easily. Using i...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.

Approximation orders of shift-invariant subspaces of L p (IR d), 2 p 1, generated by the shifts of one compactly supported function are considered. In that course, explicit approximation maps are constructed. The approach avoids quasi-interpolation and applies to stationary and non-stationary reenements. The general results are specialized to box spline spaces, to obtain new results on their ap...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we consider the properties of monotonicity-preserving and global conservation preserving for ...

Quasi-interpolation is a important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain Πm = Πm(IR ) the d–variate polynomials of degree ≤ m. In particular, the reproduction of Πm leads to an approximation order of m + 1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the ...

We generalize the transfinite triangular interpolant of (Nielson, 1987) in order to generate visually smooth (not necessarily polynomial) local interpolating quasi-optimal triangular spline surfaces. Given as input a triangular mesh stored in a half-edge data structure, at first we produce a local interpolating network of curves by optimizing quadratic energy functionals described along the arc...