Abstract— This paper introduces a new set of orthogonal moments function hypergeometric based on the discrete Legendre polynomials. The Legendre moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain o...

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ball...

Abstract In this paper, we study the Legendre wavelets for the solution of linear, nonlinear and singular Fredholm integral equations of second kind using approximation technique. The properties of Legendre wavelets together with the Gaussian integration method are used to reduce the problem to the solution of algebraic equations. The main purpose of this article is to discuss the theoretical a...

Student, Assistant Professor Associate Professor Lendi Institute of Engineering and Technology, VZM, INDIA. Abstract: The peak side lobe level (PSL) is numerically estimated for Rudin-shapiro sequences and Legendre sequences which belong to the families of Binary sequences. Notable similarities are presented between PSL and merit factor behavior under cyclic rotations of the sequences (i.e. 1/4...

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

Predictive complexity is a generalisation of Kolmogorov complexity. In this paper we point out some properties of predictive complexity connected with the Legendre ({Young{Fenchel) transformation. Our main result is that mixability is necessary for the existence of conditional predictive complexity (it is known to be su cient under very mild assumptions). We formulate a di erential criterion of...

An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to constraint systems, the procedure of finding a Hamiltonian for a singular Lagrangian is just that of solving a corresponding Clairaut equation with a subsequent application of the proposed Legendre-Clairaut transf...

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a s...

A new set of modified Legendre rational functions which are mutually orthogonal in L2(0,+∞) is introduced. Various projection and interpolation results using the modified Legendre rational functions are established. These results form the mathematical foundation of related spectral and pseudospectral methods for solving partial differential equations on the half line. A spectral scheme using th...

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...