This article considers the extension of V. A. Markov’s theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality...

This work is concerned with approximating a trivariate function defined on tensor-product domain via evaluations. Combining tensorized Chebyshev interpolation Tucker decomposition of low multilinear rank yields approximations that can be computed and stored very efficiently. The existing Chebfun3 algorithm [Hashemi Trefethen, SIAM J. Sci. Comput., 39 (2017)]uses similar format but the construct...

Image resizing is a basic tool in image processing, and literature, we have many methods based on different approaches, which are often specialized only upscaling or downscaling. In this paper, independently of the (reduced enlarged) size aim to get, approach problem at continuous scale where underlying function representing globally approximated by its Lagrange–Chebyshev I kind interpolation p...

Parton distribution functions (PDFs) are an essential ingredient for theoretical predictions at colliders. Since their exact form is unknown, handling and delivery practical applications relies on approximate numerical methods. We discuss the implementation of PDFs based a global interpolation in terms Chebyshev polynomials. demonstrate that this allows significantly higher accuracy lower compu...

A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the Fast Fourier Transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N2) operations instead of the FFT's O(N log N). This sort of "off-grid" interpolation is needed by codes which dynamically readjust the grid ...

The purpose of this survey is to present some approximation and shape preserving properties of the so-called nonlinear (more exactly sublinear) and positive, max-product operators, constructed by starting from any discrete linear approximation operators, obtained in a series of recent papers jointly written with B. Bede and L. Coroianu. We will present the main results for the max-product opera...

Stable polynomial evaluation and interpolation at n Chebyshev or adjusted (expanded) Chebyshev points is performed using O(nlog’ n) arithmetic operations, to be compared with customary algorithms either using on the order of n* operations or being unstable. We also evaluate a polynomial of degree d at the sets of n Chebyshev or adjusted (expanded) Chebyshev points using O(dlog d log n) if n 5 d...