An algorithm for a generalized Chebyshev interpolation procedure, increasing the number of sample points more moderately than doubling, is presented. The FFT for a real sequence is incorporated into the algorithm to enhance its efficiency. Numerical comparison with other existing algorithms is given.

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...

This paper presents a technique to obtain a realization for passive ladder networks of the Inverse-Chebyshev lowpass filter with all positive elements. The technique consists in the shifting of transmission zeros to infinity by means of a transformation in the complex frelquency s-plane. The technique allows for multiple frequency shifts until the desired realization is obtained. Results show t...

This monograph covers some recent advances in a range of acceleration techniques frequently used convex optimization. We first use quadratic optimization problems to introduce two key families methods, namely momentum and nested schemes. They coincide the case form Chebyshev method. discuss methods detail, starting with seminal work Nesterov structure convergence proofs using few master templat...

Keywords: Set-valued mapping Chebyshev center Uniformly convex Locally uniformly convex Chebyshev fixed point a b s t r a c t The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and th...