• Title/Summary/Keyword: Legendre wavelet

Search Result 2, Processing Time 0.017 seconds

An Efficient Computational Method for Linear Time-invariant Systems via Legendre Wavelet (르장드르 웨이블릿을 이용한 선형 시불변 시스템의 효율적 수치 해석 방법)

  • Kim, Beomsoo
    • Journal of Institute of Control, Robotics and Systems
    • /
    • v.19 no.7
    • /
    • pp.577-582
    • /
    • 2013
  • In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet's integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

AN EFFICIENT AND STABLE ALGORITHM FOR NUMERICAL EVALUATION OF HANKEL TRANSFORMS

  • Singh, Om P.;Singh, Vineet K.;Pandey, Rajesh K.
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.5_6
    • /
    • pp.1055-1071
    • /
    • 2010
  • Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.