Markov's inequality and the existence of an extension operator for C∞ functions
Journal of Approximation Theory
Bernstein theorems for elliptic equations
Journal of Approximation Theory
Bernstein type theorems for compact sets in Rnrevisited
Journal of Approximation Theory
On Bernstein and Markov-type inequalities for multivariate polynomials on convex bodies
Journal of Approximation Theory
A local version of the Pawłucki-Pleśniak extension operator
Journal of Approximation Theory
Numerical Mathematics (Texts in Applied Mathematics)
Numerical Mathematics (Texts in Applied Mathematics)
Bivariate Lagrange interpolation at the Padua points: The generating curve approach
Journal of Approximation Theory
Computing approximate Fekete points by QR factorizations of Vandermonde matrices
Computers & Mathematics with Applications
Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle
Journal of Computational and Applied Mathematics
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
SIAM Journal on Numerical Analysis
Full length article: On optimal polynomial meshes
Journal of Approximation Theory
Computing Fekete and Lebesgue points: Simplex, square, disk
Journal of Computational and Applied Mathematics
On the generation of symmetric Lebesgue-like points in the triangle
Journal of Computational and Applied Mathematics
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We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximants. For analytic functions, similar results may be achieved on more general K by allowing the number of points to grow at a slightly larger rate.