Related papers: Randomized Joint Diagonalization of Symmetric Matr…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
Approximate joint diagonalization of a set of matrices provides a powerful framework for numerous statistical signal processing applications. For non-unitary joint diagonalization (NUJD) based on the least-squares (LS) criterion, outliers,…
Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…
Learning the joint probability of random variables (RVs) is the cornerstone of statistical signal processing and machine learning. However, direct nonparametric estimation for high-dimensional joint probability is in general impossible, due…
We introduce two families of random tridiagonal block matrices for which the joint eigenvalue distributions can be computed explicitly. These distributions are novel within random matrix theory, and exhibit interactions among eigenvalue…
Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's pioneering 1969 paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
Randomized SVD has become an extremely successful approach for efficiently computing a low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp (SIREV 2011) contains extensive analysis, and has made it a…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. Recently, [BGVKS, FOCS 2020] proved that a (non-Hermitian) matrix can be diagonalized with a randomized algorithm in $O(n^{\omega}\log^2(n/\epsilon))$…
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…
This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact---a situation we refer to as "mismatched adjoint". We show that the method may…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair $\{A,L\}$, where we propose three approaches to compute approximate generalized singular…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…