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...

In this paper, interval Legendre wavelet method is investigated to approximated the solution of the interval Volterra-Fredholm-Hammerstein integral equation. The shifted interval Legendre polynomials are introduced and based on interval Legendre wavelet method is defined. The existence and uniqueness theorem for the interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examp...

The continuous orthogonal polynomials, such as Zernike and pseudo-Zernike, are often used as an expansion of corneal height data. However, the use of continuous polynomials has some limitations due to the discretization. It is because that the integrals are usually approximated by discrete summations, and this process not only leads to numerical errors, but also severely affects some analytical...

in this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (scs, cells/ml) collected by animal breeding center of iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. models with different order of legendre polynomials were compared using bayesian information criterion (bic).for milk, fat yield and scs genetic an...

Applying the theorems of Mobius inverse and Dirichlet inverse, a general algorithm to obtain biorthogonal functions based on generalized Fourier series analysis is introduced. In the algorithm, the orthogonal function can be not only Fourier or Legendre series, but also can be any one of all orthogonal function systems. These kinds of biorthogonal function sets are used as scramble signals to c...

in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated usi...

Suppose that the first m Fourier coefficients of a piecewise analytic function are given. Direct expansion in a Fourier series suffers from the Gibbs phenomenon and lacks uniform convergence. Nonetheless, in this paper we show that, under very broad conditions, it is always possible to recover an n-term expansion in a different system of functions using only these coefficients. Such an expansio...

Spectral methods approximate functions by projection onto a space PN of orthogonal polynomials of degree ≤ N . When the underlying function is periodic trigonometric (Fourier) polynomials are employed while a popular choice for non-periodic functions are the Chebyshev polynomials. Legendre polynomials are another option in the non-periodic case but are not as popular in applications due to the ...

Orthogonal polynomials on the semicircle were introduced by Gautschi and Milovanović in [Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (July 1985), pp. 179-185] [J. Approx. Theory, 46 (1986), 230-250]. In this paper we give an account of kind orthogonality, weighted generalizations mainly oriented to Chebyshev weights first second kinds, including several interesting properties such pol...

LetL be a big holomorphic line bundle on a compact complex manifoldX.We show how to associate a convex function on the Okounkov body ofL to any continuous metric e−ψ on L.We will call this the Chebyshev transform of ψ, denoted by c[ψ]. Our main theorem states that the integral of the difference of the Chebyshev transforms of two weights is equal to the relative energy of the weights, which is a...