
Approximate solution of the integral equations involving kernel with additional singularity
The paper is devoted to the approximate solutions of the Fredholm integr...
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A Chebyshevbased Highorderaccurate Integral Equation Solver for Maxwell's Equations
This paper introduces a new method for discretizing and solving integral...
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Generalized attenuated ray transforms and their integral angular moments
In this article generalized attenuated ray transforms (ART) and integral...
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Deep kernel learning for integral measurements
Deep kernel learning refers to a Gaussian process that incorporates neur...
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An explicit numerical algorithm to the solution of Volterra integral equation of the second kind
This paper considers a numeric algorithm to solve the equation y(t)...
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Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
We consider GMRES applied to discretisations of the highfrequency Helmh...
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Improved Asymptotics for Zeros of Kernel Estimates via a Reformulation of the LeadbetterCryer Integral
The expected number of false inflection points of kernel smoothers is ev...
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Separability of the kernel function in an integral formulation for anisotropic radiative transfer equation
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The integral formulation consists of a coupled system of integral equations for the angular moments of the transport solution. We analyze the approximate separability of the kernel functions in these integral formulations, deriving asymptotic lower and upper bounds on the number of terms needed in a separable approximation of the kernel functions as the moment grows. Our analysis provides the mathematical understanding on when lowrank approximations to the discretized integral kernels can be used to develop fast numerical algorithms for the corresponding system of integral equations.
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