in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...

An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator using sum of squares polynomial optimization. It is easily parallelized exploiting the sparsity of the neighborhood structure of the underlying spline space; as a result, it is ve...

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally...

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute refinement mask of B-splines any order in case general scaling factor. Our is solely derived from reproduction properties satisfied by splines it does not require explicit construction or evaluation basis functions. The second part discusses factorization B-spline masks terms a...

Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...

The map H → H↓ assigns to each finite-dimensional space of smooth functions a homogeneous polynomial space of the same dimension. We discuss applications of this map in the areas of multivariate polynomial interpolation, box spline theory and polynomial ideals. §

Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing wor...

generalized solution on neumann problem of the fourth order ordinary dierential equation in space w2 (0; b) has been discussed , we obtain the condition on b.v.p when the solution is in classical form. formulation of quintic spline function has been derived and the consistency relations are given.numerical method,based on quintic spline approximation has been developed. spline solution of the...

We establish rigorously the fundamental nesting behavior of T-spline spaces in terms of the topology of the T-mesh. This provides a theoretical foundation for local refinement algorithms based on analysis-suitable T-splines and their use in isogeometric analysis. A key result is a dimension formula for smooth polynomial spline spaces defined over the Bézier mesh of a T-spline.