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- W1503708287 abstract "We are interested in the verification of Newton’s method. We use a formalization of the convergence and stability of the method done with the axiomatic real numbers of Coq’s Standard Library in order to validate the computation with Newton’s method done with a library of exact real arithmetic based on co-inductive streams. The contribution of this work is twofold. Firstly, based on Newton’s method, we design and prove correct an algorithm on streams for computing the root of a real function in a lazy manner. Secondly, we prove that rounding at each step in Newton’s method still yields a convergent process with an accurate correlation between the precision of the input and that of the result. An algorithm including rounding turns out to be much more efficient.KeywordsTheorem ProveExact ComputationProof AssistantInitial IterationLazy EvaluationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W1503708287 created "2016-06-24" @default.
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- W1503708287 date "2009-01-01" @default.
- W1503708287 modified "2023-09-24" @default.
- W1503708287 title "Formal Verification of Exact Computations Using Newton’s Method" @default.
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- W1503708287 doi "https://doi.org/10.1007/978-3-642-03359-9_28" @default.
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