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In this paper we propose an approximation method for high-dimensional $1$-periodic functions based on the multivariate ANOVA decomposition. We provide an analysis on the classical ANOVA decomposition on the torus and prove some important…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…
In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$,…
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive…
It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…
The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire…
The Rapid Iterative FiTting (RIFT) parameter inference algorithm provides a simulation-based inference approach to efficient, highly-parallelized parameter inference for GW sources. Previous editions of RIFT have conservatively optimized…
We propose an improvement of the known DFT-based indexing technique for fast retrieval of similar time sequences. We use the last few Fourier coefficients in the distance computation without storing them in the index since every coefficient…
We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…
This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…
High-order numerical methods for solving elliptic equations over arbitrary domains typically require specialized machinery, such as high-quality conforming grids for finite elements method, and quadrature rules for boundary integral…
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…
As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…
The numerical evaluation of integrals of the form \begin{align*} \int_a^b f(x) e^{ikg(x)}\,dx \end{align*} is an important problem in scientific computing with significant applications in many branches of applied mathematics, science and…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
We propose a general technique for improving alternating optimization (AO) of nonconvex functions. Starting from the solution given by AO, we conduct another sequence of searches over subspaces that are both meaningful to the optimization…