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pro vyhledávání: '"65d15"'
Autor:
Buttsworth, Timothy, Hodgkinson, Liam
We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\mathsf{O}(3)\times\mathsf{O}(10)$ on $S^{12}\subset \mathbb{R}^{13}= \mathbb{R}^3\oplus \mathbb{R}^{10}$. The proof invo
Externí odkaz:
http://arxiv.org/abs/2412.01184
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of dimensionality we u
Externí odkaz:
http://arxiv.org/abs/2411.03989
Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great success of S
Externí odkaz:
http://arxiv.org/abs/2410.10533
Autor:
Levin, David
Publikováno v:
Advances in Quantum Chemistry. Vol. 68. Academic Press, 2014. 19-42
Given function values on a domain $D_0$, possibly with noise, we examine the possibility of extending the function to a larger domain $D$, $D_0\subset D$. In addition to smoothness at the boundary of $D_0$, the extension on $D\setminus D_0$ should al
Externí odkaz:
http://arxiv.org/abs/2410.09423
We consider the task of data-driven identification of dynamical systems, specifically for systems whose behavior at large frequencies is non-standard, as encoded by a non-trivial relative degree of the transfer function or, alternatively, a non-trivi
Externí odkaz:
http://arxiv.org/abs/2410.02000
In this contribution, we introduce the multiplicative Jacobi polynomials that arise as one of the solutions of the multiplicative Sturm-Liouville equation \begin{equation*} \frac{d^*}{dx}\left( e^{(1-x^2)\omega(x)}\odot \frac{d^*y}{dx} \right)\oplus
Externí odkaz:
http://arxiv.org/abs/2410.01009
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function by a purpo
Externí odkaz:
http://arxiv.org/abs/2409.14278
The problem of multi-task regression over graph nodes has been recently approached through Graph-Instructed Neural Network (GINN), which is a promising architecture belonging to the subset of message-passing graph neural networks. In this work, we di
Externí odkaz:
http://arxiv.org/abs/2409.08023
We consider the approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix over a continuum compact domain. Our approach is based on approximating the smallest eigenvalue by the one obtained by projecting the large matri
Externí odkaz:
http://arxiv.org/abs/2409.05791
Autor:
Anand, Akash, Nainwal, Prakash
The FC-Gram trigonometric polynomial approximation of a non-periodic function that interpolates the function on equispaced grids was introduced in 2010 by Bruno and Lyon [J. Comput. Phys, 229(6):2009-2033, 2010]. Since then, the approximation algorit
Externí odkaz:
http://arxiv.org/abs/2409.00722