Best Summation Formulae and Discrete Splines

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1973 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 10, pages 448-459 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Mangasarian, O. L.; Schumaker, L. L.;

doi: 10.1137/0710039

Best Summation Formulae and Discrete Splines

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Abstract

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.

Keywords

Numerical mathematical programming methods, Acceleration of convergence in numerical analysis, Numerical computation using splines

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