Browsing by Author "Gander, Martin J."

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    A Gentle Introduction to Interpolation on the Grassmann Manifold
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2024) Ciaramella, Gabriele; Gander, Martin J.; Vanzan, Tommaso
    [no abstract available]
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    Is it possible to predict the far future before the near future is known accurately?
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2019) Gander, Martin J.
    It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict the future. However, to make accurate predictions can require extremely large amounts of computation. If we need seven days to compute a prediction for the weather tomorrow and the day after tomorrow, the prediction arrives too late and is thus not a prediction any more. Although it may seem improbable, with the advent of powerful computers with many parallel processors, it is possible to compute a prediction for tomorrow and the day after tomorrow simultaneously. We describe a mathematical algorithm which is designed to achieve this.
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    Review of the methods of reflections
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Ciaramella, Gabriele; Gander, Martin J.; Halpern, Laurence; Salomon, Julien
    The methods of reflections were invented to obtain approximate solutions of the motion of more than one particle in a given environment, provided that one can represent the solution for one particle rather easily. This motivation is quite similar to the motivation of the Schwarz domain decomposition method, which was invented to prove existence and uniqueness of solutions of the Laplace equation on complicated domains, which are composed of simpler ones, for which existence and uniqueness of solutions was known. Like for Schwarz methods, there is also an alternating and a parallel method of reflections, but interestingly, the parallel method is not always convergent. We carefully trace in this paper the historical development of these methods of reflections, give several precise mathematical formulations, an equivalence result with the alternating Schwarz method for two particles, and also an analysis for a one dimensional model problem with three particles of the alternating, parallel, and a recent averaged parallel method of reflections.