A constructive proof of Simpson's Rule

Details A constructive proof of Simpson's Rule A constructive proof of Simpson's Rule

2012-02-15

arxiv.org/abs/1202.3460v1

Mathematics

Numerical Analysis

Scientific paper

For most purposes, one can replace the use of Rolle's theorem and the mean value theorem, which are not constructively valid, by the law of bounded change. The proof of two basic results in numerical analysis, the error term for Lagrange interpolation and Simpson's rule, however seem to require the full strength of the classical Rolle's Theorem. The goal of this note is to justify these two results constructively, using ideas going back to Amp\`ere and Genocchi.

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