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of 127
pro vyhledávání: '"Xie, Pengpeng"'
Matrix decompositions in dual number representations have played an important role in fields such as kinematics and computer graphics in recent years. In this paper, we present a QR decomposition algorithm for dual number matrices, specifically geare
Externí odkaz:
http://arxiv.org/abs/2404.13525
By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of their rows an
Externí odkaz:
http://arxiv.org/abs/2301.13163
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient algorithm for comp
Externí odkaz:
http://arxiv.org/abs/2203.12491
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order singular v
Externí odkaz:
http://arxiv.org/abs/2203.02761
Publikováno v:
In Applied Mathematics Letters October 2024 156
Publikováno v:
In Journal of Computational and Applied Mathematics 1 January 2025 453
Autor:
Cao, Zhengbang, Xie, Pengpeng
Solving linear discrete ill-posed problems for third order tensor equations based on a tensor t-product has attracted much attention. But when the data tensor is produced continuously, current algorithms are not time-saving. Here, we propose an incre
Externí odkaz:
http://arxiv.org/abs/2111.14449
In this note, we present perturbation analysis for the T-product based tensor singular values defined by Lu et al. First, the Cauchy's interlacing-type theorem for tensor singular values is given. Then, the inequalities about the difference between t
Externí odkaz:
http://arxiv.org/abs/2109.11194
Autor:
Cao, Zhengbang, Xie, Pengpeng
In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known a
Externí odkaz:
http://arxiv.org/abs/2108.03892
Autor:
Cao, Zhengbang, Xie, Pengpeng
This paper establishes some perturbation analysis for the tensor inverse, the tensor Moore-Penrose inverse and the tensor system based on the t-product. In the settings of structured perturbations, we generalize the Sherman-Morrison-Woodbury (SMW) fo
Externí odkaz:
http://arxiv.org/abs/2107.09544