arXiv subjects

Phung Van Manh

Publications and source records attributed to Phung Van Manh.

3 recordsLinked to original sources

arXiv2012

On the Convergence of Kergin and Hakopian Interpolants at Leja Sequences for the Disk

We prove that Kergin interpolation polynomials and Hakopian interpolation polynomials at the points of a Leja sequence for the unit disk $D$ of a sufficiently smooth function $f$ in a neighbourhood of $D$ converge uniformly to $f$ on $D$. Moreover, when $f$ is $C^\infty$ on $D$, all the derivatives of the interpolation polynomials converge uniformly to the corresponding derivatives of $f$.

math.CA↗

arXiv2011

On the Continuity of Multivariate Lagrange Interpolation at Chung-Yao Lattices

We give a natural geometric condition that ensures that sequences of Chung-Yao interpolation polynomials (of fixed degree) of sufficiently differentiable functions converge to a Taylor polynomial.

math.NA↗

arXiv2011

Lagrange interpolation at real projections of Leja sequences for the unit disk

We show that the Lebesgue constant of the real projection of Leja sequences for the unit disk grows like a polynomial. The main application is the first construction of explicit multivariate interpolation points in $[-1,1]^N$ whose Lebesgue constant also grows like a polynomial.

math.NA↗