Related papers: A Note On Estimating the Spectral Norm of A Matrix…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein's…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
We present a simple randomized algorithm for approximate matrix multiplication (AMM) whose error scales with the *output* norm $\|AB\|_F$. Given any $n\times n$ matrices $A,B$ and a runtime parameter $r\leq n$, the algorithm produces in…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes…
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
Power iteration can improve the accuracy of randomized SVD, but requires multiple data passes, making it impractical in streaming or memory-constrained settings. We introduce a lightweight yet effective sketch-power iteration, allowing…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
A model-independent method is proposed to characterize and correct charge sharing spectral distortions in energy-resolved X-ray acquisitions with pixellated photon-counting detectors. The technique is based on the determination of a…
Light spectra are a very important source of information for diverse classification problems, e.g., for discrimination of materials. To lower the cost for acquiring this information, multispectral cameras are used. Several techniques exist…
This paper studies two potential modifications of XTrace (Epperly et al., SIMAX 45(1):1-23, 2024), a randomized algorithm for estimating the trace of a matrix. The first is a variance reduction step that averages the output of XTrace over…
The spectrum of a real and symmetric $N\times N$ matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work we…