We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N . This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This is the first of a series of papers in this area, which solves the longstanding problem of finding a satisfactory mul...

This paper proposes a new efficiency benchmarking methodology that is capable of incorporating probability while still preserving the advantages of a distribution-free and nonparametric modeling technique. This new technique developed in this paper will be known as the DEA-Chebyshev model. The foundation of DEA-Chebyshev model is based on the model pioneered by Charnes, Cooper, and Rhodes in 19...

The classical column generation approach often shows a very slow convergence. Many different acceleration techniques have beenproposed recently to improve the convergence. Here, we briefly survey these methods and propose a novel algorithm based on the Chebyshev center of the dual polyhedron. The Chebyshev center can be obtained by solving a linear program; consequently, the proposed method can...

The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

in this note, we characterize chebyshev subalgebras of unital jb-algebras. we exhibit that if b is chebyshev subalgebra of a unital jb-algebra a, then either b is a trivial subalgebra of a or a= h r .l, where h is a hilbert space

Large, sparse nonsymmetric systems of linear equations with a matrix whose eigenvalues lie in the right half plane may be solved by an iterative method based on Chebyshev polynomials for an interval in the complex plane. Knowledge of the convex hull of the spectrum of the matrix is required in order to choose parameters upon which the iteration depends. Adaptive Chebyshev algorithms, in which t...

The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coeffi...

A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov– Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always st...

In this paper, we present some new variants of Chebyshev-Halley methods free from second derivative for solving nonlinear equation of the type f(x) = 0, and show that the convergence orders of the proposed methods are three or four. Several numerical examples are given to illustrate the efficiency and performance of the new methods.