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Abstract: This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made. [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]

Abstract: This paper presents a compensated algorithm to accurately evaluate a polynomial expressed in Chebyshev basis of the first and second kind with floating-point coefficients. The principle is to apply error-free transformations to improve the traditional Clenshaw algorithm. The new algorithm is as accurate as the Clenshaw algorithm performed in twice the working precision. Forward error analysis and numerical experiments illustrate the accuracy and properties of the proposed algorithm. [Copyright &y& Elsevier]

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

Abstract: The paper develops algorithmic methods to enumerate all normal subgroups of a finitely presented group such that the factor groups are either isomorphic to or to . The case of two generators is treated in detail. A range of examples starting with the free group on two generators and ending with groups having only finitely many normal subgroups of this type is discussed. [Copyright &y& Elsevier]