Results 11 to 20 of about 256,120 (256)
Randomized Rank-Revealing QLP for Low-Rank Matrix Decomposition
IEEE Access, 2023 The pivoted QLP decomposition is computed through two consecutive pivoted QR decompositions. It is an approximation to the computationally prohibitive singular value decomposition (SVD). This work is concerned with a partial QLP decomposition of matrices
Maboud F. Kaloorazi +4 more
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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 more
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Low-Rank Updates of Matrix Functions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2018 We consider the task of updating a matrix function $f(A)$ when the matrix $A\in{\mathbb C}^{n \times n}$ is subject to a low-rank modification. In other words, we aim at approximating $f(A+D)-f(A)$ for a matrix $D$ of rank $k \ll n$. The approach proposed in this paper attains efficiency by projecting onto tensorized Krylov subspaces produced by matrix-
Bernhard Beckermann +2 more
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Quantization for low-rank matrix recovery [PDF]
Information and Inference: A Journal of the IMA, 2018 Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root ...
Eric Lybrand, Rayan Saab
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Sensitivity of low-rank matrix recovery
Numerische Mathematik, 2022 We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix by a low-rank matrix. We give an algorithm for computing the associated condition number and demonstrate experimentally
Breiding, Paul, Vannieuwenhoven, Nick
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A Nonconvex Method to Low-Rank Matrix Completion
IEEE Access, 2022 In recent years, the problem of recovering a low-rank matrix from partial entries, known as low-rank matrix completion problem, has attracted much attention in many applications.
Haizhen He +3 more
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Sparse and Low-Rank Matrix Decompositions [PDF]
IFAC Proceedings Volumes, 2009 Abstract Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, but obtaining an exact solution is NP-hard in general.
Venkat Chandrasekaran +3 more
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On a Low-Rank Matrix Single-Index Model
Mathematics, 2023 In this paper, we conduct a theoretical examination of a low-rank matrix single-index model. This model has recently been introduced in the field of biostatistics, but its theoretical properties for jointly estimating the link function and the ...
The Tien Mai
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Global Optimality in Low-Rank Matrix Optimization [PDF]
IEEE Transactions on Signal Processing, 2017 This paper considers the minimization of a general objective function $f(X)$ over the set of rectangular $n\times m$ matrices that have rank at most $r$. To reduce the computational burden, we factorize the variable $X$ into a product of two smaller matrices and optimize over these two matrices instead of $X$. Despite the resulting nonconvexity, recent
Zhihui Zhu +3 more
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Nonconvex Robust Low-Rank Matrix Recovery [PDF]
SIAM Journal on Optimization, 2020 In this paper we study the problem of recovering a low-rank matrix from a number of random linear measurements that are corrupted by outliers taking arbitrary values. We consider a nonsmooth nonconvex formulation of the problem, in which we explicitly enforce the low-rank property of the solution by using a factored representation of the matrix ...
Xiao Li 0009 +3 more
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