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A learnable activation function based on orthogonal Legendre wavelets
International Journal of Wavelets, Multiresolution and Information ProcessingActivation functions play a crucial role in introducing nonlinearity into neural networks. Previous approaches, such as rectifying neurons and logistic sigmoid neurons, primarily focused on constructing activation functions based on biological models. These methods have achieved considerable success in various machine learning tasks. However, they are
Yan Ye, Zhi Liu
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Legendre wavelets method for solving differential equations of Lane–Emden type
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Two-dimensional Legendre wavelets and operational matrices of integration
2005Summary: One-dimensional Legendre wavelets are the basis of a numerical method for solving one-dimensional variational problems and integral equations. In this paper we introduce two-dimensional Legendre wavelets. These wavelets are defined over the interval \([0,1]\times[0,1]\) and an orthonormal set over this interval.
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A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets
Applied Mathematical Modelling, 2013Siraj-ul-Islam, Imran Aziz
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Techniques for solving integral and differential equations by Legendre wavelets
International Journal of Systems Science, 2009Xiaofan Yang
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