Zobrazeno 1 - 10
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pro vyhledávání: '"Cavoretto, R"'
Background: Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency remains a cha
Externí odkaz:
http://arxiv.org/abs/2407.07375
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the co
Externí odkaz:
http://arxiv.org/abs/2403.18017
Autor:
Cavoretto, R., Dell'Accio, F., De Rossi, A., Di Tommaso, F., Siar, N., Sommariva, A., Vianello, M.
We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, PUM). This approach gives a promising alternative to other recent metho
Externí odkaz:
http://arxiv.org/abs/2307.07203
Publikováno v:
In Computers and Mathematics with Applications 15 June 2024 164:12-20
Publikováno v:
In Applied Mathematics and Computation 1 July 2023 448
The partition of unity (PU) method, performed with local radial basis function (RBF) approximants, has already been proved to be an effective tool for solving interpolation or collocation problems when large data sets are considered. It decomposes th
Externí odkaz:
http://arxiv.org/abs/1811.05193
Autor:
Cavoretto, R., De Rossi, A.
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on the construc
Externí odkaz:
http://arxiv.org/abs/1811.04710
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can also provi
Externí odkaz:
http://arxiv.org/abs/1803.10673
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local ap
Externí odkaz:
http://arxiv.org/abs/1607.03278
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally suppo
Externí odkaz:
http://arxiv.org/abs/1604.04585