Related papers: Projection-based QLP Algorithm for Efficiently Com…

The pivoted QLP decomposition is computed through two consecutive pivoted QR decompositions, and provides an approximation to the singular value decomposition. This work is concerned with a partial QLP decomposition of low-rank matrices…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\times n$ efficiently such that $A\approx QLP$, where $L$ is the rank-$k$…

In this paper, we introduce a randomized QLP decomposition called Rand-QLP. Operating on a matrix $\bf A$, Rand-QLP gives ${\bf A}={\bf QLP}^T$, where $\bf Q$ and $\bf P$ are orthonormal, and $\bf L$ is lower-triangular. Under the…

In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually…

Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such…

The randomly pivoted partial Cholesky algorithm (RPCholesky) computes a factorized rank-k approximation of an N x N positive-semidefinite (psd) matrix. RPCholesky requires only (k + 1) N entry evaluations and O(k^2 N) additional arithmetic…

Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…