A new method is proposed for designing IIR digital allpass filters with an equiripple phase response that can be proven to be optimal in the Chebyshev sense. The proposed procedure is based on the formulation of an eigenvalue problem by using the Remez exchange algorithm. Since there exists more than one eigenvalue in the general eigenvalue problem, we introduce a new and very simple selection ...

In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses collocation scheme quasi-linearization. First, Taylor expansion around differential equations of system used obtain set perturbation equations. Second, first-order necessary conditions for OCPs the...

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomia...

A numerical method based on Chebyshev polynomials and local interpolating functions is proposed for solving the onedimensional parabolic partial differential equation subject to non-classical conditions. To assess its validity and accuracy, the method is applied to solve several test problem. 2007 Elsevier Inc. All rights reserved.

The requirement that a Chebyshev quadrature formula have distinct real nodes is not always compatible with the requirement that the degree of precision of an npoint formula be at least equal to n. This condition may be expressed as | \d\ \p = 0, 1 g p, where d (dx, ■ ■ ■ , d„) with Mo(w) ~ , -IT dj = 2w A iM ; = 1, 2, • • ■ , z!, ZJ ,_, Pj(io), j = 0, 1, • • • , are the moments of the weight fu...

Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...

It is an important fact that general families of Chebyshev and L-splines can be locally represented, i.e. there exists a basis of B-splines which spans the entire space. We develop a special technique to calculate with 4 order Chebyshev splines of minimum deficiency on nonuniform meshes, which leads to a numerically stable algorithm, at least in case one special Hermite interpolant can be const...

Let μ be a probability measure on the real line with finite moments of all orders. Suppose the linear span of polynomials is dense in L(μ). Then there exists a sequence {Pn}∞ n=0 of orthogonal polynomials with respect to μ such that Pn is a polynomial of degree n with leading coefficient 1 and the equality (x − αn)Pn(x) = Pn+1(x) + ωnPn−1(x) holds, where αn and ωn are SzegöJacobi parameters. In...