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We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter…

Data Structures and Algorithms · Computer Science 2023-06-06 Ameya Velingker , Maximilian Vötsch , David P. Woodruff , Samson Zhou

The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…

Data Structures and Algorithms · Computer Science 2019-02-28 Michael Kapralov , Ameya Velingker , Amir Zandieh

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,…

Signal Processing · Electrical Eng. & Systems 2021-05-31 Kai Wu , J. Andrew Zhang , Xiaojing Huang , Y. Jay Guo

The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…

Image and Video Processing · Electrical Eng. & Systems 2022-12-09 T. L. T. da Silveira , D. R. Canterle , D. F. G. Coelho , V. A. Coutinho , F. M. Bayer , R. J. Cintra

We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the…

Computational Geometry · Computer Science 2023-09-19 Lorenzo Diazzi , Daniele Panozzo , Amir Vaxman , Marco Attene

The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…

Numerical Analysis · Mathematics 2017-08-14 Santhosh Karnik , Zhihui Zhu , Michael B. Wakin , Justin Romberg , Mark A. Davenport

In this paper we demonstrate the methodology for parallelizing the computation of large one-dimensional discrete fast Fourier transforms (DFFTs) on multi-core Intel Xeon processors. DFFTs based on the recursive Cooley-Tukey method have to…

Mathematical Software · Computer Science 2016-07-12 Ryo Asai , Andrey Vladimirov

The discrete cosine transform (DCT) is the key step in many image and video coding standards. The 8-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, 16-point DCT…

Multimedia · Computer Science 2017-02-08 F. M. Bayer , R. J. Cintra , A. Edirisuriya , A. Madanayake

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

This paper presents an efficient approach for multiplierless implementation for eight-point DCT approximation, which based on coordinate rotation digital computer (CORDIC) algorithm. The main design objective is to make critical path of…

Hardware Architecture · Computer Science 2011-11-01 Maxim Vashkevich , Marek Parfieniuk , Alexander Petrovsky

We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\dots,x_n)$ over $R^n$ and a parameter $\epsilon> 0$, our…

Computational Complexity · Computer Science 2013-12-02 Anindya De , Rocco Servedio

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Numerical Analysis · Mathematics 2020-06-24 Lutz Kämmerer , Felix Krahmer , Toni Volkmer

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more…

Numerical Analysis · Mathematics 2015-08-07 Jeremy Axelrod

The discrete Hartley transform (DHT) is a useful tool for medical image coding. The three-dimensional DHT (3D DHT) can be employed to compress medical image data, such as magnetic resonance and X-ray angiography. However, the computation of…

Signal Processing · Electrical Eng. & Systems 2022-06-02 V. A. Coutinho , F. M. Bayer , R. J. Cintra

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that…

Optimization and Control · Mathematics 2022-08-09 Yongchun Li , Marcia Fampa , Jon Lee , Feng Qiu , Weijun Xie , Rui Yao

We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…

Numerical Analysis · Mathematics 2019-09-06 Lutz Kämmerer

A low-complexity 8-point orthogonal approximate DCT is introduced. The proposed transform requires no multiplications or bit-shift operations. The derived fast algorithm requires only 14 additions, less than any existing DCT approximation.…

Multimedia · Computer Science 2017-02-06 F. M. Bayer , R. J. Cintra

The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…

Quantum Physics · Physics 2026-03-18 Junaid Aftab , Yuehaw Khoo , Haizhao Yang

A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…

Numerical Analysis · Mathematics 2021-04-21 Ion Victor Gosea , Stefan Güttel

A multiply-accumulate (MAC) operation is the main computation unit for DSP applications. DSP blocks are one of the efficient solutions to implement MACs in FPGA's. However, since the DSP blocks have wide multiplier and adder blocks, MAC…

Hardware Architecture · Computer Science 2021-10-26 Ercan Kalali , Rene van Leuken