Discrete linear Chebyshev approximation

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

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...

Optimal FIR and IIR Hilbert Transformer Design Via LS and Minimax Fitting

The usual way of the implementation of on-line discrete Hilbert transformers is the design of linear phase finite impulse response (FIR) filters. Recently, a method has been published for the design of infinite impulse response (IIR) Hilbert transformers as well. The paper introduces a new method for the design of both FIR and IIR Hilbert transformers, based on a parameter estimation method for...

Reduction of Linear Programming to Linear Approximation

It is well known that every l∞ linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to an l∞ linear approximation problem. Now we recall relevent definitions. An affine function of variables x1, . . . , xn is b0 + c1x1 + · · · + cnxn where b0, ci are given numbers. A linear constraint is any of the following c...

Chebyshev Centers and Approximation in Pre-Hilbert C*-Modules