Chebyshev approximation by exponential-polynomial products

Distributed Signal Processing via Chebyshev Polynomial Approximation

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We...

Real Polynomial Chebyshev Approximation by the Carathiodory - Fejir Method

A new method is presented for near-best approximation of a real function F on [-r, r] by a polynomial of degree m. The method is derived by transplanting the given problem to the unit disk, then applying the Carath6odory-Fej6r theorem. The resulting near-best approximation is constructed from the principal eigenvalue and eigenvector of a Hankel matrix of Chebyshev coefficients of F. It is well ...

Chebyshev Polynomial Approximation to Approximate Partial Differential Equations

This pa per suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, e...

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

Chebyshev polynomial approximation for transductive learning on graphs