This is to certify that I have examined a copy of a technical report by Kazh Brito and found it satisfactory in all respects, and that any and all revisions required by the examining committee have been made. Abstract This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of realistic parameters, corresponding to the requirements of numerical integration to an accuracy of about 100 to 100 000 bits. Our algorithm com...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

Supply chain demand prediction plays a very important role for enterprises to realize sales and markets management target effectively, especially for fresh agricultural product enterprises. A new model for supply chain demand prediction for fresh agricultural product enterprises is presented based on improved BP neural network. First the advantages and disadvantages of BP neural network algorit...

A new approach to find the approximate solution and the optimal control of linear time-invariant scaled systems using the Legendre wavelets is proposed. The operational matrix of stretch is derived and together with the operational matrix of integration have been used to change the system of state equations into a set of algebraic equations which can be solved using a digital computer. The appr...

We introduce a new approach in order to construct a wavelets with arbitrary support on the interval. This result allows us to adapt on the interval some important classes of wavelets (coiflets, symlets, Lemarié's wavelets). In addition, we show how to obtain multiresolution analysis on the interval with better approximation rate in some neighborhood of the interval.

Abstract. We propose the application of hyperbolic interpolatory wavelets for large-scale -dimensional data fitting. In particular, we show how wavelets can be used as a highly efficient tool for multidimensional smoothing. The grid underlying these wavelets is a sparse grid. The hyperbolic interpolatory wavelet space of level uses basis functions and it is shown that under sufficient smoothnes...