The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the r...

we consider an approximation scheme using haar wavelets for solving a class of infinite horizon optimal control problems (ocp's) of nonlinear interconnected large-scale dynamic systems. a computational method based on haar wavelets in the time-domain is proposed for solving the optimal control problem. haar wavelets integral operational matrix and direct collocation method are utilized to ...

In this work, wavelets are used in the analysis of medical images, where efficiency mathematics field has been proven because basis proposed work is newly constructed mathematical equations, and through MATLAB program, many programs have designed to be ready for use image study. Physical samples were selected that compressed using wavelets, good results obtained prove method used.

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families wavelets. this paper, we provide a possible theoretical explanation for the empirical success Specifically, show that these are optimal with respect to any optimality criterion satisfies natural properties scale- and shift-invariance.

In 1999, Dubuc and Merrien introduced a Hermite subdivision scheme which gives C-interpolants on a rectangular mesh. In this paper a two parameter version of this scheme is analyzed, and C-convergence is proved for a range of the two parameters. By introducing a control grid the parameters in the scheme can be chosen so that the interpolant inherits positivity and/or directional monotonicity fr...

We study the smoothness of the limit function for one dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midway as is usually the case. For the natural generalization of the four point scheme introduced by Dubuc and Dyn, Levin, and Gregory, we show th...