Related papers: FFT-Based Fast Computation of Multivariate Kernel …
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
Fourier and related transforms is a family of algorithms widely employed in diverse areas of computational science, notoriously difficult to scale on high-performance parallel computers with large number of processing elements (cores). This…
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…
Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…
Communication efficiency is a widely recognised research problem in Federated Learning (FL), with recent work focused on developing techniques for efficient compression, distribution and aggregation of model parameters between clients and…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
We describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing the input random field of the system using the model…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
Fast Fourier Transforms (FFTs) are exploited in a wide variety of fields ranging from computer science to natural sciences and engineering. With the rising data production bandwidths of modern FFT applications, judging best which…
In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the…
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…