Výsledky vyhledávání - Numerical methods for low-rank matrix approximation

Efficient quaternion CUR method for low-rank approximation to quaternion matrix Autor Wu, Pengling, Kou, Kit Ian, Cai, Hongmin, Yu, Zhaoyuan

“…The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing…”
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Computing low‐rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods Autor Kandolf, Peter, Koskela, Antti, Relton, Samuel D., Schweitzer, Marcel

“… We present several different Krylov subspace methods for computing low‐rank approximations of Lf(A,E…”
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Novel alternating update method for low rank approximation of structured matrices Autor Bai, Jianchao, Li, Jicheng, Dai, Pingfan

“…This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm…”
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Low rank approximation of the symmetric positive semidefinite matrix Autor Duan, Xuefeng, Li, Jiaofen, Wang, Qingwen, Zhang, Xinjun

“… Finally, we use the nonlinear conjugate gradient method with exact line search to compute the optimal low rank symmetric positive semidefinite approximation of the given matrix…”
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A Hierarchical Low-Rank Approximation Based Network Solver for EMT Simulation Autor Zhang, Lu, Wang, Bin, Zheng, Xiangtian, Shi, Weiping, Kumar, P. R., Xie, Le

“… Based on this observation, we propose a novel low-rank approximation method which permits <inline-formula><tex-math notation="LaTeX">{O(N \log N)}</tex-math></inline-formula…”
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Fast Parallel Randomized QR with Column Pivoting Algorithms for Reliable Low-Rank Matrix Approximations Autor Xiao, Jianwei, Gu, Ming, Langou, Julien

“…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…”
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Implementation improvements and extensions of an ODE-based algorithm for structured low-rank approximation Autor Fazzi, Antonio, Markovsky, Ivan, Usevich, Konstantin

“… Some extensions of the numerical method to variations of the classical structured low-rank approximation problems are then proposed…”
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Tensor approximation of the self-diffusion matrix of tagged particle processes Autor Dabaghi, Jad, Ehrlacher, Virginie, Strössner, Christoph

“…The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid…”
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Randomized methods for dynamical low-rank approximation Autor Carrel, Benjamin

“…[Display omitted] We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra…”
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A generalized Nyström method with subspace iteration for low-rank approximations of large-scale nonsymmetric matrices Autor Wang, Yatian, Wu, Nian-Ci, Liu, Yuqiu, Xiang, Hua

“…In numerical linear algebra, finding the low-rank approximation of large-scale nonsymmetric matrices is a core problem…”
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Practical Sketching Algorithms for Low-Rank Matrix Approximation Autor Tropp, Joel A., Yurtsever, Alp, Udell, Madeleine, Cevher, Volkan

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Implementation improvements and extensions of an ODE-based algorithm for structured low-rank approximation: Implementation improvements and extensions Autor Fazzi, Antonio, Markovsky, Ivan, Usevich, Konstantin

“… Some extensions of the numerical method to variations of the classical structured low-rank approximation problems are then proposed…”
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Approximation Newton method for low-rank matrix completion: Approximation Newton method for low-rank matrix completion Autor Wang, Peng, Zhu, Detong

“…In this paper, we propose an approximation Newton method for solving the low-rank matrix completion problem…”
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Generalized low-rank approximation to the symmetric positive semidefinite matrix Autor Chang, Haixia, Li, Chunmei, Liu, Longsheng

“…In this paper, we consider the generalized low-rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $ \underset{X}{\min} \sum^{m}_{i = 1}\left \Vert A_{i}-B_{i}XB_{i}^{T}\right \Vert^{2}_{F}, $ where $ X…”
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Robust Video Restoration by Joint Sparse and Low Rank Matrix Approximation Autor Ji, Hui, Huang, Sibin, Shen, Zuowei, Xu, Yuhong

“…This paper presents a new patch-based video restoration scheme. By grouping similar patches in the spatiotemporal domain, we formulate the video restoration problem as a joint sparse and low-rank matrix approximation problem…”
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Low-Rank Matrix Approximation with Manifold Regularization Autor Zhang, Zhenyue, Zhao, Keke

“…This paper proposes a new model of low-rank matrix factorization that incorporates manifold regularization to the matrix factorization…”
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Randomized low‐rank approximation of parameter‐dependent matrices Autor Kressner, Daniel, Lam, Hei Yin

“…This work considers the low‐rank approximation of a matrix A(t)$$ A(t) $$ depending on a parameter t$$ t $$ in a compact set D⊂ℝd$$ D\subset {\mathbb{R}}^d…”
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Low rank tensor methods in Galerkin-based isogeometric analysis Autor Mantzaflaris, Angelos, Jüttler, Bert, Khoromskij, Boris N., Langer, Ulrich

“…The global (patch-wise) geometry map, which describes the computational domain, is a new feature in isogeometric analysis. This map has a global tensor…”
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Sparse principal component analysis via regularized low rank matrix approximation Autor Shen, Haipeng, Huang, Jianhua Z.

“… (SVD) of the data matrix and extract the PCs through solving a low rank matrix approximation problem…”
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Quasioptimal alternating projections and their use in low-rank approximation of matrices and tensors Autor Budzinskiy, Stanislav

“… The theory is motivated by the successful application of alternating projections to low-rank matrix and tensor approximation…”
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