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  1. On the Epistemological Analysis of Modeling and Computational Error in the Mathematical Sciences.Nicolas Fillion & Robert M. Corless - 2014 - Synthese 191 (7):1451-1467.
    Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...)
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    Concepts of Solution and the Finite Element Method: A Philosophical Take on Variational Crimes.Nicolas Fillion & Robert M. Corless - 2021 - Philosophy and Technology 34 (1):129-148.
    Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...)
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    Backward Error Analysis for Perturbation Methods.Robert M. Corless & Nicolas Fillion - 2019 - In James Robert Brown, Shaoshi Chen, Robert M. Corless, Ernest Davis, Nicolas Fillion, Max Gunzburger, Benjamin C. Jantzen, Daniel Lichtblau, Yuri Matiyasevich, Robert H. C. Moir, Mark Wilson & James Woodward (eds.), Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 Acmes Conferences. Springer New York. pp. 35-79.
    We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps the most important is that backward error analysis can be used to demonstrate the validity of the solution, however obtained and by whichever method. This includes a nontrivial safeguard against slips, blunders, or bugs in the original computation. We also demonstrate its utility in deciding (...)
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    Algorithms and Complexity in Mathematics, Epistemology, and Science: Proceedings of 2015 and 2016 Acmes Conferences.Nicolas Fillion, Robert M. Corless & Ilias S. Kotsireas (eds.) - 2019 - Springer New York.
    ACMES is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including (...)
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