Best Summation Formulae and Discrete Splines
Olvi L. Mangasarian, Larry L. Schumaker · SIAM Journal on Numerical Analysis · 1973
The problem of obtaining a best summation formula for a finite sequence of real numbers in terms of a fixed number of terms of the sequence is reduced to a solvable linear or quadratic programming problem. This is done by developing the appropriate discrete Taylor and Peano theorems. The best summation formulae are related to discrete splines studied earlier. Discrete monosplines are introduced here and related to best summation formulae. Some numerical results are given.