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In this article, a spectral collocation method based on the Chebyshev polynomials is investigated for the approximate solution of a class of neutral functional-differential equations with variable coefficients, which have many applications in mathematical physics. A Chebyshev collocation method based on Chebyshev Gauss-Lobatto quadrature points is utilized to reduce the solution of such problem to a system of algebraic equations. In addition, accurate approximation is obtained by selecting few Chebyshev Gauss-Lobatto collocation points. Comparing the numerical results with those of known techniques shows that the present method is better in terms of accuracy over the other methods mentioned in this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers a new method for FIR filters design. The method uses an L ∞ optimality norm. To achieve a better approximating effect, a new modulating function which compresses the oscillations of the cosine is proposed. A parameter sets the gradient of the modulating function, with respect to the oscillations’ compression. The approximating polynomial is carried out using Remez’ exchange algorithm. An optimal polynomial with lowest possible (four) degree, that approximates an ideal filter''s response with high precision is proposed. With the proposed method a FIR filter with arbitrary specifications can be designed. Design examples of FIR filters with a minimization of calculation are performed. The obtained filter''s responses are close to the ideal response. The design examples demonstrate that the proposed approach may be a good alternative in several applications. [Copyright &y& Elsevier]

In this paper, we consider a rational algorithm for modification of a positive measure by quadratic factor, , where it is allowed z to be in supp(d σ). Also, we present an application of modified algorithm to the measures and , where T 2(t)=t 2−½ is the second degree monic Chebyshev polynomial of the first kind and , , is the Chebyshev measure of the second kind. Also, we present an application to the constrained L 2-polynomial approximation. [ABSTRACT FROM AUTHOR]

In this paper, we derive an algorithm to solve the linear quadratic (LQ) optimal regulator problems. The new approach is based on efficient Legendre and Chebyshev formulae at the Chebyshev-Gauss-Lobatto points. The technique enjoys advantages of both the Legendre and Chebyshev approximations near the end points. To show the numerical behavior of the proposed method, the simulation results of an example are presented. [ABSTRACT FROM AUTHOR]

A new algorithm is developed for computing etAB, where A is an n x n matrix and B is n x n0 with n0 « n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n0 matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etA B or a sequence Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree, using the recent analysis of Al-Mohy and Higham [SIAM J. Matrix Anal. Appl., 31 (2009), pp. 970 989], which provides sharp truncation error bounds expressed in terms of the quantities ||Ak