An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

Scalar multiplication on Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic cur...

We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data co...

Forest biomass stock and spatial distribution are still unknown parameters for many regions of the world. Today’s information is largely based on ground measurements on a plot basis without remote regions coverage. Thus, a method capable of quantifying biomass by means of Remote Sensing could help to reduce these uncertainties and contribute to a better understanding of the carbon cycle (Hought...

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...