Optimal interpolation with incomplete polynomials (Q1059240)

The problem of interpolation occupies an important position in the field of numerical methods and analysis. Here the author attempts with considerable success to obtain the optimal results for interpolation using suitable incomplete polynomials. The generalization of equi- oscillation conjectures of earlier workers is formulated. Two theorems with proof summarise the detailed discussions. Also the possibility of extending the methods for proving conclusions in interpolations in terms of trigonometric polynomials on closed intervals is briefly examined.