相关论文: A Randomized Multivariate Matrix Pencil Method for…
We design a fast implicit real QZ algorithm for eigenvalue computation of structured companion pencils arising from linearizations of polynomial rootfinding problems. The modified QZ algorithm computes the generalized eigenvalues of an…
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…
Linearization is a standard method in the computation of eigenvalues and eigenvectors of matrix polynomials. In the last decade a variety of linearization methods have been developed in order to deal with algebraic structures and in order…
The emergence of ultra-wideband (UWB) and high-throughput signals has necessitated advancements in data sampling technologies1. Sub-Nyquist sampling methods, such as the modulated wideband converter (MWC) and compressed auto-correlation…
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of…
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
Compressed sensing applied to magnetic resonance imaging (MRI) allows to reduce the scanning time by enabling images to be reconstructed from highly undersampled data. In this paper, we tackle the problem of designing a sampling mask for an…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…
Photoacoustic tomography is a hybrid biomedical technology, which combines the advantages of acoustic and optical imaging. However, for the conventional image reconstruction method, the image quality is affected obviously by artifacts under…
A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
Given a matrix A \in R^{m x n}, we present a randomized algorithm that sparsifies A by retaining some of its elements by sampling them according to a distribution that depends on both the square and the absolute value of the entries. We…