We bound the dimension of xed degree real algebraic interpolatory spline spaces. For a given planar triangulation T real algebraic splines interpolate speciied zi values at the vertices vi = (xi; yi) of T. For a three dimensional simplicial complex ST , real algebraic splines interpolate the boundary vertices vj = (xj; yj; zj) of ST. The main results of this paper are lower bounds on the dimens...

Published 1. End Conditions for Interpolatory Septic Spline Ghazala Akram and Shahid S. Siddiqi, International Journal of Computer Mathematics, Vol. 82, No. 12, 2005 pp15251540. 2. Solutions of Fifth Order Boundary-Value Problems Using NonPolynomial Spline Technique Shahid S. Siddiqi and Ghazala Akram, Applied Mathematics and Computation Vol. 175, No. 2, 2006 pp. 1574-1581. 3. Solutions of Sixt...

Nowadays it is accepted that the friction force is a combined effect arising from various phenomena: adhesive forces, capillary forces, contact elasticity, topography, surface chemistry, and generation of a third body, etc. Any of them can dominate depending on the experimental force and length scales of the study. Typical forces in macro-tribology are in the Newtons, while are reduced to milli...

We characterize the dimension of fixed degree functional and implicit algebraic splines in three dimensional (x,y,z) space. For a a given planar triangulation T both functional and implicit algebraic splines interpolate specified Zi values at the vertices Vi = (XitY;) of T. For a three dimensional triangulation 57 the implicit algebraic splines interpolate the boundary vertices Vj = (Xj, Yj I Z...

In this paper, we shall discuss how to construct multidimensional biorthogonal wavelets by employing a coset by coset (CBC) algorithm. We shall construct biorthogonal wavelets on the hexagonal lattice by CBC algorithm. In particular, we shall propose a CBC algorithm to construct inter-polatory biorthogonal wavelets which are derived from pairs of fundamental reenable functions. More precisely, ...

The theory of matrix subdivision schemes provides tools for the analysis of general uniform stationary matrix schemes The special case of Hermite interpolatory subdivision schemes deals with re nement algorithms for the function and the derivatives values with matrix masks depending upon the re nement level i e non stationary matrix masks Here we rst show that a Hermite interpolatory subdivisio...

This paper develops an interpolatory framework for weighted-H2 model reduction of MIMO dynamical systems. A new representation of the weighted-H2 inner products in MIMO settings is introduced and used to derive associated first-order necessary conditions satisfied by optimal weighted-H2 reduced-order models. Equivalence of these new interpolatory conditions with earlier Riccati-based conditions...

We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in R2. Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples...

Net subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc-Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interp...

The objective of this paper is to introduce a general scheme for the construction of interpolatory approximation formulas and compactly supported wavelets by using spline functions with arbitrary (nonuniform) knots. Both construction procedures are based on certain “optimally local” interpolatory fundamental spline functions which are not required to possess any approximation property.