Zobrazeno 1 - 10
of 866
pro vyhledávání: '"41a15"'
Autor:
Pijls, Henk, Phuong, Quan Le
In this paper, we propose a closed-form solution to the inverse problem in interpolation with periodic uniform B-spline curves. This solution is obtained by modifying the one we have established to a similar problem with relaxed uniform B-spline curv
Externí odkaz:
http://arxiv.org/abs/2412.07227
Autor:
Huang, Changcun
A neural network with one hidden layer or a two-layer network (regardless of the input layer) is the simplest feedforward neural network, whose mechanism may be the basis of more general network architectures. However, even to this type of simple arc
Externí odkaz:
http://arxiv.org/abs/2411.06728
Autor:
Lu, Ran
Interpolatory filters are of great interest in subdivision schemes and wavelet analysis. Due to the high-order linear-phase moment property, interpolatory refinement filters are often used to construct wavelets and framelets with high-order vanishing
Externí odkaz:
http://arxiv.org/abs/2411.04485
Autor:
Han, Bin, Michelle, Michelle
This paper introduces a wavelet Galerkin method for solving two-dimensional elliptic interface problems of the form in $-\nabla\cdot(a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface within $\Omega$. The variable scalar
Externí odkaz:
http://arxiv.org/abs/2410.16596
Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in applications
Externí odkaz:
http://arxiv.org/abs/2409.11078
Autor:
Schaback, Robert
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. They may serve as optimized basis functions in interpolation or approxima
Externí odkaz:
http://arxiv.org/abs/2409.01759
We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but critical component of a transformer becomes a natural development of an old
Externí odkaz:
http://arxiv.org/abs/2408.09624
Autor:
Buhmann, Martin, Dai, Feng
Publikováno v:
Jaen Journal of Approximation 7 (2015), 203-230
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from their linea
Externí odkaz:
http://arxiv.org/abs/2407.05772
We consider the problem of one-dimensional function approximation using shallow neural networks (NN) with a rectified linear unit (ReLU) activation function and compare their training with traditional methods such as univariate Free Knot Splines (FKS
Externí odkaz:
http://arxiv.org/abs/2407.02153
Autor:
Xu, Hailun, Kang, Hongmei
Subdivision surfaces are considered as an extension of splines to accommodate models with complex topologies, making them useful for addressing PDEs on models with complex topologies in isogeometric analysis. This has generated a lot of interest in t
Externí odkaz:
http://arxiv.org/abs/2404.18102