We generalize the univariate divided difference to a multivariate setting by considering linear combinations of point evaluations that annihilate the null space of certain differential operators. The relationship between such a linear functional and polynomial interpolation resembles that between the divided difference and Lagrange interpolation. Applying the functional to the shifted multivari...

In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control p...

We study the reconstruction of cardinal splines f(t), from their average samples yn = f ∗h(n), n ∈ Z, when the average function h(t) has support in [−1/2, 1/2]. We investigate the existence and uniqueness of the solution of the following problem: for given dates yn, find a cardinal spline f(t), of a given degree, satisfying yn = f ∗ h(n), n ∈ Z. 1 Spline interpolation and average sampling First...

We prove that the Toeplitz binary value matrix inversion associated with mth order E-spline interpolation can be implemented using only 2 (m + 1) additions. We develop pipelined architectures for real time B-spline interpolation based on simple running average filters. We also show that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can b...