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Advances in Computational Mathematics - Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data.... 相似文献
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Jean-Pierre Crouzeix Nadezda Sukhorukova Julien Ugon 《Journal of Optimization Theory and Applications》2017,172(3):950-964
In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation. 相似文献
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In this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers. 相似文献
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Crouzeix Jean-Pierre Sukhorukova Nadezda Ugon Julien 《Set-Valued and Variational Analysis》2020,28(1):123-147
Set-Valued and Variational Analysis - One of the purposes in this paper is to provide a better understanding of the alternance property which occurs in Chebyshev polynomial approximation and... 相似文献
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Aghili Alireza Sukhorukova Nadezda Ugon Julien 《Journal of mathematical chemistry》2021,59(9):2049-2062
Journal of Mathematical Chemistry - The non-isothermal analysis of materials with the application of the Arrhenius equation involves temperature integration. If the frequency factor in the... 相似文献
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In this paper, a new algorithm to locally minimize nonsmooth functions represented as a difference of two convex functions
(DC functions) is proposed. The algorithm is based on the concept of codifferential. It is assumed that DC decomposition of
the objective function is known a priori. We develop an algorithm to compute descent directions using a few elements from
codifferential. The convergence of the minimization algorithm is studied and its comparison with different versions of the
bundle methods using results of numerical experiments is given. 相似文献
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