Evaluating sums of multivariate Gaussian kernels is a key computational task in many problems in computational statistics and machine learning. The computational cost of the direct evaluation of such sums scales as the product of the number of kernel functions and the evaluation points. The fast Gauss transform proposed by Greengard and Strain (1991) is a 2-exact approximation algorithm that re...

Evaluating sums of multivariate Gaussian kernels is a key computational task in many problems in computational statistics and machine learning. The computational cost of the direct evaluation of such sums scales as the product of the number of kernel functions and the evaluation points. The fast Gauss transform proposed by Greengard and Strain (1991) is a ǫ-exact approximation algorithm that re...

We construct a fast method, OðN logNÞ, for the computation of discrete Gauss transforms with complex parameters, capable of dealing with unequally spaced grid points. The method is based on Fourier techniques, and in particular it makes use of a modified unequally spaced fast Fourier transform algorithm, in combination with previously suggested divide and conquer strategies for ordinary fast Ga...

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method ...

In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those varieties we calculate values of Hypergeometric series on certain CM points. Our methods is based on the calculation of the Picard-Fuchs equations in higher dimen...

We construct complete nonorientable minimal surfaces whose Gauss map omits two points of RP 2 . This result proves that Fujimoto’s theorem is sharp in nonorientable case.

Using satellite altimetry derived mean sea level (MSL), geopotential coefficients in terms of ellipsoidal harmonics from recent satellite gravimetry missions, gravity potential values over a grid consisting of 33,486 points at global sea areas are computed and the mean value of the gravity potential at MSL is calculated as a new geoid’s potential value. In this way we have exactly followed the ...

Local projection methods which yield c'm_1) piecewise polynomials of order m + k as approximate solutions of a boundary value problem for an mth order ordinary differential equation are determined by the k linear functional at which the residual error in each partition interval is required to vanish on. We develop a condition on these k f unctionals which implies breakpoint superconvergence (of...

using satellite altimetry derived mean sea level (msl), geopotential coefficients in terms of ellipsoidal harmonics from recent satellite gravimetry missions, gravity potential values over a grid consisting of 33,486 points at global sea areas are computed and the mean value of the gravity potential at msl is calculated as a new geoid’s potential value. in this way we have exactly followed the ...

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For continuous entropy analysis to hold and ensure Galilean invariance in technique, system requires use of non-conservat...