Barycentric formulae for some optimal rational approximants involving Blaschke products
If the value Lf of some bounded linear functional L for \(f\in H^ 2(D)\) is to be approximated, optimal formulas often refer to rational approximation. The evaluation of the interpolant can be performed by O(n) operations if a precalculation (with \(0(n^ 2)\) operations) has been done. On the other hand, some formulas for this process may be sensitive to rounding errors. This sensitivity is reduced by refering to barycentric coordinates. Moreover the connection between some formulas of \textit{F. Stenger} [Math. Comput. 47, 225-252 (1986; Zbl 0592.41019)] and of \textit{F. M. Larkin} [Approx., Theory and Appl. Proc. Int. Symp. Tampa/Florida 1976, 257-288 (1977; Zbl 0368.41032)] are elucidated.
scientific article; zbMATH DE number 4164003
scientific article