Related papers: The computation of average kernel with Gauss-Lague…
To address the computational challenges posed by nonlinear collision kernels in the Smoluchowski equation, this study proposes a universal preprocessing algorithm for the average kernel method based on the Gauss-Laguerre quadrature for…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
This paper deals with the computation of the Lerch transcendent by means of the Gauss-Laguerre formula. An a priori estimate of the quadrature error, that allows to compute the number of quadrature nodes necessary to achieve an arbitrary…
We consider the computation of the matrix logarithm by using numerical quadrature. The efficiency of numerical quadrature depends on the integrand and the choice of quadrature formula. The Gauss--Legendre quadrature has been conventionally…
A method for analytical computation of the double surface integrals for all layer potential kernels associated with the Laplace Green's function, in the Galerkin boundary element method (BEM) in $\mathbb{R}^3$ using piecewise constant flat…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex…
Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
In this paper, we study the generalized Clifford-Fourier transform introduced in [6] using the Laplace transform technique. We give explicit expressions in the even dimensional case, we obtain polynomial bounds for the kernel functions and…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an…
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we…
Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…
In this paper, we propose and analyze a product integration method for the second-kind integral equation with weakly singular and continuous kernels on the unit sphere $\mathbb{S}^2$. We employ quadrature rules that satisfy the…
Integral transform approaches are numerous in many fields of physics, but in most cases limited to the use of the Laplace kernel. However, it is well known that the inversion of the Laplace transform is very problematic, so that the…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
With the rise of big data sets, the popularity of kernel methods declined and neural networks took over again. The main problem with kernel methods is that the kernel matrix grows quadratically with the number of data points. Most attempts…