On Averaging Numbers and Linear Splines
Problems of unconstrained minimization of convex functions for finding the minimal linear splines in -norm for cases and are considered. They are constructed analogically with similar problems for finding a number that is different minimally in -norm from the given numbers . If , then the non-smo...
Збережено в:
| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Ukrainian |
| Опубліковано: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
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| Онлайн доступ: | http://mcm-math.kpnu.edu.ua/article/view/174238 |
| Теги: |
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| Назва журналу: | Mathematical and computer modelling. Series: Physical and mathematical sciences |
Репозитарії
Mathematical and computer modelling. Series: Physical and mathematical sciences| Резюме: | Problems of unconstrained minimization of convex functions for finding the minimal linear splines in -norm for cases and are considered. They are constructed analogically with similar problems for finding a number that is different minimally in -norm from the given numbers . If , then the non-smooth function is used, and if then the smooth function is used. It is shown, that with a certain choice of parameter , the optimization problems generate the known methods: the method of least squares, the method of least absolute deviations, and the Chebyshev minimax method. The properties of solutions of problems with are given |
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