Related papers: Spectral Methods for Numerical Relativity
Context: The technique of disentangling has been applied to numerous high-precision studies of spectroscopic binaries and multiple stars. Although, its possibilities have not yet been fully understood and exploited. Aims: Theoretical…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vector field using orthonormal Jacobi polynomials. Under mild…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions…
We describe a novel method for blind, single-image spectral super-resolution. While conventional super-resolution aims to increase the spatial resolution of an input image, our goal is to spectrally enhance the input, i.e., generate an…
This study concerns the efficiency of time-spectral methods for numerical solution of differential equations. It is found that the time-spectral method GWRM demonstrates insensitivity to stiffness and chaoticity due to the implicit nature…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…
This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods.…
We look for spectral type differential equations for the generalized Jacobi polynomials and for the Sobolev-Laguerre polynomials. We use a method involving computeralgebra packages like Maple and Mathematica and we will give some…
We study regularity and numerical methods for two-sided fractional diffusion equations with a lower-order term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Studying the dynamical, nonlinear regime of modified theories of gravity remains a theoretical challenge that limits our ability to test general relativity. Here we consider two generally applicable, but approximate methods for treating…