Many different bases functions have been used to estimate the solution to differential equations, such as orthogonal bases [3, 4, 14, 15], wavelets [7–8] and hybrid [2, 13, 16–17]. The various systems of orthogonal functions may be classified into two categories. The first is piecewise continuous function (PCBF) to which the orthogonal systems of Walsh functions [5], Block-pulse functions [4, 1...

In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a,b)[a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have appl...

we propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. some asymptotic properties of the proposed estimator based on block thresholding are investigated. it is found that the estimators achieve optimal minimax convergence rates over large class...

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed....