During the research, use of piece-polynomial methods in digital processing images was considered. The Hermite spline function is chosen from piece-polynomials as a mathematical model signals, and construction two-variable third-order presented. An image restoration algorithm developed based on constructed model.

Higher order differential equations have always been a tedious problem to solve for the mathematicians and engineers. Different numerical techniques were carried out to obtain numerical approximations to such problems. This research work presented and illustrated a novel numerical technique to approximate the tenth-order boundary value problems (BVPs). The techniques developed in this research ...

We propose a matrix approach to the computation of Battle-Lemari e's wavelets. Since the Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a b-spline of order m. The polynomial is the symbol of an bi-innnite matrix B associated with b-spline of order 2m. We approximate B 2m by its nit...

We propose a matrix approach to the computation of BattleLemarié's wavelets. The Fourier transform of the scaling function is the product of the inverse F(x) of a square root of a positive trigonometric polynomial and the Fourier transform of a B-spline of order m . The polynomial is the symbol of a bi-infinite matrix B associated with a B-spline of order 2m . We approximate this bi-infinite ma...

The use of cubic splines, instead of polynomials, in representing static nonlinearities in block structured models is considered. A system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, is developed in which the static nonlinearity is represented by a cubic spline. The identification algorithm, based on a separable least squares Levenb...

We provide su cient conditions for the Bernstein-B ezier (BB) form of an implicitly de ned bivariate polynomial over a triangle, such that the zero contour of the polynomial de nes a smooth and single sheeted real algebraic curve segment. We call a piecewise G-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree ...

Approximation properties of the dilations of the integer translates of a smooth function, with some derivatives vanishing at infinity, are studied. The results apply to fundamental solutions of homogeneous elliptic operators and to “shifted” fundamental solutions of the iterated Laplacian. Following the approach from spline theory, the question of polynomial reproduction by quasiinterpolation i...

We introduce curvature continuous regular free form surfaces with triangular control nets These surfaces are composed of quartic box spline surfaces and are piecewise polynomial multisided patches of total degree which minimize some energy integral The B ezier nets can be computed e ciently form the spline control net by some xed masks i e matrix multiplications x Introduction Most methods know...