Results 1 to 10 of about 302,520 (264)
Low-rank matrix approximations over canonical subspaces
Journal of Numerical Analysis and Approximation Theory, 2020 In this paper we derive closed form expressions for the nearest rank-\(k\) matrix on canonical subspaces. We start by studying three kinds of subspaces. Let \(X\) and \(Y\) be a pair of given matrices. The first subspace contains all the \(m\times
Achiya Dax
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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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Structural Damage Assessment Using Multiple-Stage Dynamic Flexibility Analysis
Aerospace, 2022 Vibration-based damage assessment technology is a hot topic in aerospace engineering, civil engineering, and mechanical engineering. In this paper, a damage assessment approach using multiple-stage dynamic flexibility analysis is proposed for structural ...
Yun Sun , Qiuwei Yang, Xi Peng
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The Phaseless Rank of a Matrix
SIAM Journal on Applied Algebra and Geometry, 2021 We consider the problem of finding the smallest rank of a complex matrix whose absolute values of the entries are given. We call this minimum the phaseless rank of the matrix of the entrywise absolute values. In this paper we study this quantity, extending a classic result of Camion and Hoffman and connecting it to the study of amoebas of determinantal
António Pedro Goucha, João Gouveia
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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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Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space
Mathematics, 2023 The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems.
Dijana Mosić +2 more
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On the Redundancy in the Rank of Neural Network Parameters and Its Controllability
Applied Sciences, 2021 In this paper, we show that parameters of a neural network can have redundancy in their ranks, both theoretically and empirically. When viewed as a function from one space to another, neural networks can exhibit feature correlation and slower training ...
Chanhee Lee +5 more
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Probabilistic rank and matrix rigidity [PDF]
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017 We consider a notion of probabilistic rank and probabilistic sign-rank of a matrix, which measures the extent to which a matrix can be probabilistically represented by low-rank matrices. We demonstrate several connections with matrix rigidity, communication complexity, and circuit lower bounds, including: The Walsh-Hadamard Transform is Not Very Rigid.
Josh Alman, R. Ryan Williams
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On the rank of a random binary matrix [PDF]
The Electronic Journal of Combinatorics, 2019 We study the rank of a random $n \times m$ matrix $\mathbf{A}_{n,m;k}$ with entries from $GF(2)$, and exactly $k$ unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all ${n \choose k}$ such columns.
Colin Cooper +2 more
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Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion [PDF]
SIAM Journal on Scientific Computing, 2015 In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity.
Zheng Wang 0011 +5 more
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