A new method is presented for computation of optimal control for linear systems using Haar wavelets. The method is based on a novel operational matrix derived from integration of Haar wavelets. The optimal control problem is converted to a two-point-boundary-value problem, which is then solved using the Haar wavelet transformation. The proposed method is then extended to the numerical solution ...

The DDHFm package is designed to perform data-driven Haar-Fisz (DDHF) variance stabilization. The basic DDHF method itself is described in [4, 5]. The modifications to DDHF to make it work successfully for microarray (or indeed similar kinds of replicate data) are described in [10]. The basic idea of the Haar-Fisz transform is very simple. First, a Haar wavelet transform is applied to the data....

In this paper, we develop a novel energy-preserving wavelet collocation method for solving general multi-symplectic formulations of Hamiltonian PDEs. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, the wavelet collocation method is conducted for spatial discretization. The obtained semi-discrete system is shown to be a finite-dimensional Hamiltonian s...

The wavelet periodogram is hard to smooth because of the low signal-to-noise ratio and non-stationary covariance structure. This article introduces a method for denoising a local wavelet periodogram by applying a Haar-Fisz transform which Gaussianises and stabilizes the variance of the periodogram. Consequently the transformed periodogram is easier to smooth. This article demonstrates the super...

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This paper introduces the hybrid wavelet collocation Brinkman penalization method for solving the Navier–Stokes equations in arbitrarily complex geometries. The main advantages of the wavelet collocation method and penalization techniques are described, and a brief summary of their implementation is given. The hybrid method is then applied to a simple flow around cylinders with both periodic an...

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the ...

In order to extract the intrinsic information of climatic time series from background red noise, we will first give an analytic formula on the distribution of Haar wavelet power spectra of red noise in a rigorous statistical framework. The relation between scale aand Fourier period T for the Morlet wavelet is a= 0.97T . However, for Haar wavelet, the corresponding formula is a= 0.37T . Since fo...