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math.NA2024
The need for accuracy and smoothness in numerical simulations
Carl Christian Kjelgaard Mikkelsen, Lorién López-Villellas
We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to jud…
math.NA2023
How accurate does Newton have to be?
Carl Christian Kjelgaard Mikkelsen, Lorién López-Villellas, Pablo García-Risueño
We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any s…