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• W2154709206 abstract "We discuss a formal development for the certification of Newton's method. We address several issues encountered in the formal study of numerical algorithms: developing the necessary libraries for our proofs, adapting paper proofs to suit the features of a proof assistant and designing new proofs based on the existing ones to deal with optimisations of the method. We start from Kantorovitch's Theorem, which gives the convergence of Newton's method in the case of a system of equations. To formalise this proof inside the proof assistant Coq, we first need to code the necessary concepts from multivariate analysis. We also 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. This proof is based on Kantorovitch's Theorem, but is an original result. An algorithm including rounding is a more accurate model for computations with Newton's method in practice." @default.
• W2154709206 created "2016-06-24" @default.
• W2154709206 creator A5078094629 @default.
• W2154709206 date "2011-07-01" @default.
• W2154709206 modified "2023-09-23" @default.
• W2154709206 title "Formal proofs for theoretical properties of Newton's method" @default.
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• W2154709206 doi "https://doi.org/10.1017/s0960129511000077" @default.
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