Properties of projections obtained by averaging certain polynomial interpolants
We describe a way to compute polynomial approximants to analytic functions f(z) in the unit disk by forming the average of m polynomials of degree n−1, each of which interpolates f(z) at n equidistant points on the unit circle. The paper discusses properties of the projections so defined. Norms of these projections are calculated and the asymptotic behavior is characterized. Furthermore, these averages are used to approximate Laurent sections.
KeywordsUnit Circle Average Technique Laurent Series Lebesgue Constant Taylor Coefficient
Unable to display preview. Download preview PDF.
- 6.Erdös, P. (1968): Problems and results on the convergence and divergence of the Lagrange interpolation polynomials and some external problems. Mathematics (Cluj) 10, 64–73.Google Scholar