Related papers: Analyzing the Approximation Error of the Fast Grap…
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave representation of the Gaussian kernel and a new…
Graph signal processing has become an essential tool for analyzing data structured on irregular domains. While conventional graph shift operators (GSOs) are effective for certain tasks, they inherently lack flexibility in modeling…
The Quantum Fourier Transform (QFT) is required by hidden subgroup problem (HSP) algorithms, including Shor's algorithm for factoring. The circuit depth of the QFT remains challenging for near-term hardware. To find shallower alternatives…
Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log…
In this paper we extend the deterministic sublinear FFT algorithm in Plonka et al. (2018) for fast reconstruction of $M$-sparse vectors ${\mathbf x}$ of length $N= 2^J$, where we assume that all components of the discrete Fourier transform…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model. We test it on portfolios ranging in size from 25 (the size of DJ iTraxx Australia) to 100 (the size of DJCDX.NA.HY) with a single factor…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
The graph Laplacian is an important tool in Graph Signal Processing (GSP) as its eigenvalue decomposition acts as an analogue to the Fourier transform and is known as the Graph Fourier Transform (GFT). The line graph has a GFT that is a…
In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat.…
Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…