相关论文: Deviation Maximization for Rank-Revealing QR Facto…

We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to…

In this paper, we introduce an efficient algorithm for column subset selection that combines the column-pivoted QR factorization with sparse subspace embeddings. The proposed method, SE-QRSC, is particularly effective for wide matrices with…

We approach the Max-3-Cut problem through the lens of maximizing complex-valued quadratic forms and demonstrate that low-rank structure in the objective matrix can be exploited, leading to alternative algorithms to classical semidefinite…

Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…

Query Performance Prediction (QPP) estimates the retrieval quality of ranking models without the use of any human-assessed relevance judgements, and finds applications in query-specific selective decision making to improve overall retrieval…

A Gaussian elimination algorithm is presented that reveals the numerical rank of a matrix by yielding small entries in the Schur complement. The algorithm uses the maximum volume concept to find a square nonsingular submatrix of maximum…

In this note we describe two modifications of the ScaLAPACK subroutines PxGEQPF for computing the QR factorization with the Businger-Golub column pivoting. First, we resolve a subtle numerical instability in the same way as we have done it…

Matrix completion is one of the most challenging problems in computer vision. Recently, quaternion representations of color images have achieved competitive performance in many fields. Because it treats the color image as a whole, the…

We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix $A$, such a factorization provides a low rank approximate decomposition of the form $A \approx C U R$, where $C$ and $R$…

Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that…

Recommender system has been more and more popular and widely used in many applications recently. The increasing information available, not only in quantities but also in types, leads to a big challenge for recommender system that how to…

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is…

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…

Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…

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…

Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…

Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…

Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…

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…

Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming…