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Relevant bibliographies by topics / Frobenius-Norm

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Journal articles

Academic literature on the topic 'Frobenius-Norm'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Frobenius-Norm"

1

Cheng, Che-Man, Seak-Weng Vong, and David Wenzel. "Commutators with maximal Frobenius norm." Linear Algebra and its Applications 432, no. 1 (2010): 292–306. http://dx.doi.org/10.1016/j.laa.2009.08.008.

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2

Peng, Yang. "Inequalities for the Frobenius norm." Journal of Mathematical Inequalities, no. 2 (2015): 493–98. http://dx.doi.org/10.7153/jmi-09-43.

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3

Peng, Xi, Canyi Lu, Zhang Yi, and Huajin Tang. "Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations." IEEE Transactions on Neural Networks and Learning Systems 29, no. 1 (2018): 218–24. http://dx.doi.org/10.1109/tnnls.2016.2608834.

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4

Böttcher, Albrecht, and David Wenzel. "The Frobenius norm and the commutator." Linear Algebra and its Applications 429, no. 8-9 (2008): 1864–85. http://dx.doi.org/10.1016/j.laa.2008.05.020.

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5

Chellaboina, V., and W. M. Haddad. "Is the Frobenius matrix norm induced?" IEEE Transactions on Automatic Control 40, no. 12 (1995): 2137–39. http://dx.doi.org/10.1109/9.478340.

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6

Toutounian, F., D. Khojasteh Salkuyeh, and M. Mojarrab. "LSMR Iterative Method for General Coupled Matrix Equations." Journal of Applied Mathematics 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/562529.

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Abstract:

By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations∑k=1qAikXkBik=Ci,i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups(X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and(R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group(X1(0),X2(0),…,Xq(0)), a solution group(X1*,X2*,…,Xq*)can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group(X¯1,X¯2,…,X¯q)in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method.

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7

Yin, Feng, and Guang-Xin Huang. "An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations." Abstract and Applied Analysis 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/857284.

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Abstract:

The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics. The iterative method is an important way to solve the generalized coupled Sylvester systems. In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min over generalized reflexive matrix . For any initial generalized reflexive matrix , by the iterative algorithm, the generalized reflexive solution can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution can also be derived when an appropriate initial iterative matrix is chosen. Furthermore, the unique optimal approximate solution to a given matrix in Frobenius norm can be derived by finding the least-norm generalized reflexive solution of a new corresponding minimum Frobenius norm residual problem: with , . Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.

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8

Cui, Xiangzhao, Chun Li, Jine Zhao, Li Zeng, Defei Zhang, and Jianxin Pan. "Covariance structure regularization via Frobenius-norm discrepancy." Linear Algebra and its Applications 510 (December 2016): 124–45. http://dx.doi.org/10.1016/j.laa.2016.08.013.

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9

Huckle, T., and A. Kallischko. "Frobenius norm minimization and probing for preconditioning." International Journal of Computer Mathematics 84, no. 8 (2007): 1225–48. http://dx.doi.org/10.1080/00207160701396387.

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10

González, Luis, and Antonio Suárez. "Improving approximate inverses based on Frobenius norm minimization." Applied Mathematics and Computation 219, no. 17 (2013): 9363–71. http://dx.doi.org/10.1016/j.amc.2013.03.057.

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