Related papers: Sobolev estimates for constructive uniform-grid FF…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
The utilization of periodic structures such as photonic crystals and metasurfaces is common for light manipulation at nanoscales. One of the most widely used computational approaches to consider them and design effective optical devices is…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
In the present paper we describe a simple black box algorithm for efficiently and accurately solving scattering problems related to the scattering of time-harmonic waves from radially-symmetric potentials in two dimensions. The method uses…
The effective field theory (EFT) construction when the objects of interest are the In-In (or real time) correlators rather than the In-Out S-matrix elements is constructed. This is done using the formal equivalence between the In-In and…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
Recent progress in synthetic aperture sonar (SAS) technology and processing has led to significant advances in underwater imaging, outperforming previously common approaches in both accuracy and efficiency. There are, however, inherent…
Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…
We construct and analyze a projection-free linearly implicit method for the approximation of flows of harmonic maps into spheres. The proposed method is unconditionally energy stable and, under a sharp discrete regularity condition,…
A spherical $t$-design is a set of points on the sphere that are nodes of a positive equal weight quadrature rule having algebraic accuracy $t$ for all spherical polynomials with degrees $\le t$. Spherical $t$-designs have many…
Higher spatial resolution and larger imaging scene are always the goals pursued by advanced space-borne SAR system.High resolution and wide swath SAR imaging can provide more information about the illuminated scene of interest on one…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…