نتایج جستجو برای: legendre

تعداد نتایج: 3750  

Journal: :SIAM J. Numerical Analysis 2005
Chiu-Yen Kao Stanley Osher Yen-Hsi Richard Tsai

We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point using only its immediate neighboring grid values and is easy to implement numerically. The minimization that is related to the Legendre transform in our sweeping scheme can either be solved analytically or...

1994
JOHN ZHANG

The Müntz-Legendre polynomials arise by orthogonalizing the Müntz system {xxo, xx¡, ...} with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Müntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Lague...

1999
Ron G. van Schyndel Andrew Z. Tirkel Imants D. Svalbe

Many types of pseudo-random signals have been used to embed signatures as watermarks, with spread spectrum signal techniques used to recover the signature from the encrypted data. Legendre sequences are a suitable candidate for signature encryption as they exhibit ‘perfect’ two level auto-correlation. Additionally, Legendre sequences have the unusual and interesting property of invariance under...

2015
Baoru Han Lisha Cai Wenfeng Li

Medical information digitization makes the medical information storage and extraction more convenient. Medical image information security and copyright protection is also gradually being taken seriously, and some medical image watermarking has been applied. According to the characteristics of three-dimensional medical images, this paper proposes a robust zero-watermarking algorithm for medical ...

Journal: :Journal of Approximation Theory 2012
James Wan Wadim Zudilin

In 1951, F. Brafman derived several “unusual” generating functions of classical orthogonal polynomials, in particular, of Legendre polynomials Pn(x). His result was a consequence of Bailey’s identity for a special case of Appell’s hypergeometric function of the fourth type. In this paper, we present a generalization of Bailey’s identity and its implication to generating functions of Legendre po...

2007
S. Kazemi H. R. Hassani G. R. Dadashzadeh F. Geran

In this paper, an efficient method to obtain the elements current distribution for a non uniformly spaced array is presented. For a given far field pattern, after sampling the array factor the proposed method uses the least mean square error technique to solve the system of equations rather than solving the previously published Legendre function method. It’s shown that the average side lob leve...

2005
Hugo Touchette Christian Beck

We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave. If the spectrum has no definite concavity, then the transform yield...

2015
A. H. BHRAWY M. A. ZAKY D. BALEANU

Burgers’ equation is a fundamental partial differential equation in fluid mechanics. This paper reports a new space-time spectral algorithm for obtaining an approximate solution for the space-time fractional Burgers’ equation (FBE) based on spectral shifted Legendre collocation (SLC) method in combination with the shifted Legendre operational matrix of fractional derivatives. The fractional der...

2015
Emad M. Solouma Mohamed M. Khader E. M. Solouma M. M. Khader

This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show ...

2016
H. SABERI NAJAFI H. AMINIKHAH

In this paper, continuous Legendre multi-wavelets are utilized as a basis in a practical direct method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerica...

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