Lagrange interpolation at real projections of Leja sequences for the unit disk
arXiv:1102.3629
Originality Incremental advance
AI Analysis
Provides a theoretical guarantee for polynomial growth of Lebesgue constants in multivariate interpolation, which is a known bottleneck for high-dimensional approximation.
The authors prove that the Lebesgue constant for Leja sequences on the unit disk grows polynomially, enabling the first explicit multivariate interpolation points in [-1,1]^N with polynomial Lebesgue constant growth.
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.