Thirioux, Xavier and Maffart, Alexis
Taylor Series Revisited.
(2020)
[Report]
(Unpublished)
|
(Document in English)
PDF (Author's version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 1MB |
Abstract
We propose a renovated approach around the use of Taylor expansions to provide polynomial approximations. We introduce a coinductive type scheme and finely-tuned operations that altogether constitute an algebra, where our multivariate Taylor expansions are first-class objects. As for applications, beyond providing classical expansions of integro-differential and algebraic expressions mixed with elementary functions, we demonstrate that solving ODE and PDE in a direct way, without external solvers, is also possible. We also discuss the possibility of computing certified errors within our scheme.
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