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Journal articles on the topic 'Singular decomposition'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Caltenco, J. H., José Luis Lopez-Bonilla, B. E. Carvajal-Gámez, and P. Lam-Estrada. "Singular Value Decomposition." Bulletin of Society for Mathematical Services and Standards 11 (September 2014): 13–20. http://dx.doi.org/10.18052/www.scipress.com/bsmass.11.13.

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We study the SVD of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to pseudoinverse of Moore-Bjenhammar-Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution, and our approach gives the Lanczos classification for these systems.

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2

Кутрунов, В., and Т. Латфуллин. "НАСЛЕДОВАНИЕ СИНГУЛЯРНЫХ ВЕКТОРОВ ПРИ ПОПОЛНЕНИИ МАТРИЦЫ СТОЛБЦОМ." EurasianUnionScientists 6, no. 12(81) (January 18, 2021): 36–40. http://dx.doi.org/10.31618/esu.2413-9335.2020.6.81.1173.

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Let the matrix A1 be obtained from the matrix A by adding a column to it on the right. The possibility of inheritance of singular numbers and the corresponding singular vectors when passing from matrix A to matrix A1 is investigated. The singular value decompositions of the matrix A are based on the scalar and vector properties of the square symmetric matrices ATA and AAT. The article deals with the singular value decomposition of the matrix A, which has more rows than columns, and the decomposition is based on the analysis of the ATA matrix.

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3

Maehara, Takanori, and Kazuo Murota. "Simultaneous singular value decomposition." Linear Algebra and its Applications 435, no. 1 (July 2011): 106–16. http://dx.doi.org/10.1016/j.laa.2011.01.007.

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4

Zhang, Lingsong, and Yao Wang. "Visualizing singular value decomposition." Wiley Interdisciplinary Reviews: Computational Statistics 6, no. 3 (March 14, 2014): 197–201. http://dx.doi.org/10.1002/wics.1295.

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5

KOH, MIN-SUNG. "A QUINTET SINGULAR VALUE DECOMPOSITION THROUGH EMPIRICAL MODE DECOMPOSITIONS." Advances in Adaptive Data Analysis 06, no. 02n03 (April 2014): 1450010. http://dx.doi.org/10.1142/s1793536914500101.

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A particular quintet singular valued decomposition (Quintet-SVD) is introduced in this paper via empirical mode decompositions (EMDs). The Quintet-SVD results in four specific orthogonal matrices with a diagonal matrix of singular values. Furthermore, this paper shows relationships between the Quintet-SVD and traditional SVD, generalized low rank approximations of matrices (GLRAM) of one single matrix, and EMDs. One application of the Quintet-SVD for speech enhancement is shown and compared with an application of traditional SVD.

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6

Lem, Kong Hoong. "Truncated singular value decomposition in ripped photo recovery." ITM Web of Conferences 36 (2021): 04008. http://dx.doi.org/10.1051/itmconf/20213604008.

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Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.

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7

Cai, Jian-Feng, and Stanley Osher. "Fast singular value thresholding without singular value decomposition." Methods and Applications of Analysis 20, no. 4 (2013): 335–52. http://dx.doi.org/10.4310/maa.2013.v20.n4.a2.

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8

Chen, Zhen, Lifeng Qin, Shunbo Zhao, Tommy HT Chan, and Andy Nguyen. "Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification." Advances in Structural Engineering 22, no. 12 (May 22, 2019): 2687–98. http://dx.doi.org/10.1177/1369433219849817.

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This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decomposition algorithm extracts the useful responses from truncated small singular values and superposes it into the solution of truncated singular value decomposition, which can be useful in moving force identification. In this article, a comprehensive numerical simulation is set up to evaluate piecewise polynomial truncated singular value decomposition, and compare this technique against truncated singular value decomposition and singular value decomposition. Numerically simulated data are processed to validate the novel method, which show that regularization matrix [Formula: see text] and truncating point [Formula: see text] are the two most important governing factors affecting identification accuracy and ill-posedness immunity of piecewise polynomial truncated singular value decomposition.

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9

Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." Quantum 5 (June 29, 2021): 483. http://dx.doi.org/10.22331/q-2021-06-29-483.

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Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

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10

Gass, S. I., and T. Rapcsák. "Singular value decomposition in AHP." European Journal of Operational Research 154, no. 3 (May 2004): 573–84. http://dx.doi.org/10.1016/s0377-2217(02)00755-5.

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11

smithies, Laura, and Richard S. Varga. "Singular value decomposition Geršgorin sets." Linear Algebra and its Applications 417, no. 2-3 (September 2006): 370–80. http://dx.doi.org/10.1016/j.laa.2005.10.032.

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12

Zhang, Xue, Xiangfeng Meng, Xiulun Yang, Yurong Wang, Yongkai Yin, Xianye Li, Xiang Peng, Wenqi He, Guoyan Dong, and Hongyi Chen. "Singular value decomposition ghost imaging." Optics Express 26, no. 10 (May 4, 2018): 12948. http://dx.doi.org/10.1364/oe.26.012948.

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13

Gu, Ming, and Stanley C. Eisenstat. "Downdating the Singular Value Decomposition." SIAM Journal on Matrix Analysis and Applications 16, no. 3 (July 1995): 793–810. http://dx.doi.org/10.1137/s0895479893251472.

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14

De Lathauwer, Lieven, Bart De Moor, and Joos Vandewalle. "A Multilinear Singular Value Decomposition." SIAM Journal on Matrix Analysis and Applications 21, no. 4 (January 2000): 1253–78. http://dx.doi.org/10.1137/s0895479896305696.

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15

Brake, Danielle A., Jonathan D. Hauenstein, Frank-Olaf Schreyer, Andrew J. Sommese, and Michael E. Stillman. "Singular Value Decomposition of Complexes." SIAM Journal on Applied Algebra and Geometry 3, no. 3 (January 2019): 507–22. http://dx.doi.org/10.1137/18m1189270.

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16

Davies, Philip I., and Matthew I. Smith. "Updating the singular value decomposition." Journal of Computational and Applied Mathematics 170, no. 1 (September 2004): 145–67. http://dx.doi.org/10.1016/j.cam.2003.12.039.

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17

Van Huffel, Sabine. "Partial singular value decomposition algorithm." Journal of Computational and Applied Mathematics 33, no. 1 (December 1990): 105–12. http://dx.doi.org/10.1016/0377-0427(90)90260-7.

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18

Wang, Xiaoqiang, Lejia Gu, Heung-wing Lee, and Guofeng Zhang. "Quantum tensor singular value decomposition*." Journal of Physics Communications 5, no. 7 (July 1, 2021): 075001. http://dx.doi.org/10.1088/2399-6528/ac0d5f.

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19

Antoniou, I., and S. A. Shkarin. "Decay spectrum and decay subspace of normal operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 6 (December 2001): 1245–55. http://dx.doi.org/10.1017/s0308210500001372.

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Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators Ap, Aac and Asc such that there exists an orthonormal basis of eigenvectors for the operator Ap, the operator Aac has purely absolutely continuous spectrum and the operator Asc has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component Asc into a direct sum of two self-adjoint operators and . The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

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20

Wu, Chunfu. "Essential Matrix Decomposition without Dependence of Singular Value Decomposition." Journal of Information and Computational Science 12, no. 8 (May 20, 2015): 3299–309. http://dx.doi.org/10.12733/jics20105949.

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21

Bentbib, A. H., and A. Kanber. "Block Power Method for SVD Decomposition." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 2 (June 1, 2015): 45–58. http://dx.doi.org/10.1515/auom-2015-0024.

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Abstract We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = Uk∑kVkT , where ∑k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1≥ σ2 ⋯ ≥ σk. Uk and Vk are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.

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22

Cheng, Gang, Hongyu Li, Xiao Hu, Xihui Chen, and Houguang Liu. "Fault diagnosis of gearbox based on local mean decomposition and discrete hidden Markov models." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 14 (March 10, 2016): 2706–17. http://dx.doi.org/10.1177/0954406216638885.

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This paper proposes an intelligent diagnosis method for gearbox using local mean decomposition and discrete hidden Markov models, including local mean decomposition, the energy difference spectrum of singular value, multiscale sample entropy, and the discrete hidden Markov model. How to extract feature information effectively and identify the fault type is key to making a diagnosis in the presence of strong noise. Combined with the Kurtosis criterion and correlation coefficient, the product function that contains the main characteristic frequency is filtered out by local mean decomposition. Next, the filtered local mean decompositions are used to construct the Hankel matrix and complete singular value decomposition. The denoised and reconstructed signals are achieved by an energy difference spectrum of singular value. Furthermore, the feature information after denoising is extracted by multiscale sample entropy. After combining the discrete hidden Markov models, the mechanical condition is identified. Practical examples of diagnoses for four gear types used in the gearbox can accurately identify the gear types, and the recognition rates of the various types are above 92%. The experiments shown here verify the effectiveness of the method proposed in this paper.

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23

KUME, KENJI. "INTERPRETATION OF SINGULAR SPECTRUM ANALYSIS AS COMPLETE EIGENFILTER DECOMPOSITION." Advances in Adaptive Data Analysis 04, no. 04 (October 2012): 1250023. http://dx.doi.org/10.1142/s1793536912500239.

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Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.

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24

Rong Hu, Weihong Xu, and Fangjun Kuang. "An Improved Incremental Singular Value Decomposition." International Journal of Advancements in Computing Technology 4, no. 2 (February 15, 2012): 95–102. http://dx.doi.org/10.4156/ijact.vol4.issue2.13.

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25

seshaiah, Mr B. Venkata, Ms Roopadevi K N, and Stafford Michahial. "Image Compression using Singular Value Decomposition." IJARCCE 5, no. 12 (December 30, 2016): 208–11. http://dx.doi.org/10.17148/ijarcce.2016.51246.

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26

Hong, Zhaoping, and Heng Lian. "Sparse-smooth regularized singular value decomposition." Journal of Multivariate Analysis 117 (May 2013): 163–74. http://dx.doi.org/10.1016/j.jmva.2013.02.011.

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27

Akritas, Alkiviadis G., and Gennadi I. Malaschonok. "Applications of singular-value decomposition (SVD)." Mathematics and Computers in Simulation 67, no. 1-2 (September 2004): 15–31. http://dx.doi.org/10.1016/j.matcom.2004.05.005.

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28

Newman, Matthew, and Prashant D. Sardeshmukh. "A Caveat Concerning Singular Value Decomposition." Journal of Climate 8, no. 2 (February 1995): 352–60. http://dx.doi.org/10.1175/1520-0442(1995)008<0352:accsvd>2.0.co;2.

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29

Evans, D. J. "The QIF Singular Value Decomposition Method." International Journal of Computer Mathematics 79, no. 5 (January 2002): 637–45. http://dx.doi.org/10.1080/00207160210957.

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30

Paige, C. C. "Computing the Generalized Singular Value Decomposition." SIAM Journal on Scientific and Statistical Computing 7, no. 4 (October 1986): 1126–46. http://dx.doi.org/10.1137/0907077.

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31

Grasedyck, Lars. "Hierarchical Singular Value Decomposition of Tensors." SIAM Journal on Matrix Analysis and Applications 31, no. 4 (January 2010): 2029–54. http://dx.doi.org/10.1137/090764189.

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32

Bai, Zhaojun, and James W. Demmel. "Computing the Generalized Singular Value Decomposition." SIAM Journal on Scientific Computing 14, no. 6 (November 1993): 1464–86. http://dx.doi.org/10.1137/0914085.

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33

MASTORAKIS, NIKOS E. "Singular value decomposition in multidimensional arrays." International Journal of Systems Science 27, no. 7 (July 1996): 647–50. http://dx.doi.org/10.1080/00207729608929261.

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34

Lee, Mihee, Haipeng Shen, Jianhua Z. Huang, and J. S. Marron. "Biclustering via Sparse Singular Value Decomposition." Biometrics 66, no. 4 (February 16, 2010): 1087–95. http://dx.doi.org/10.1111/j.1541-0420.2010.01392.x.

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35

Zhang, Lingsong, J. S. Marron, Haipeng Shen, and Zhengyuan Zhu. "Singular Value Decomposition and Its Visualization." Journal of Computational and Graphical Statistics 16, no. 4 (December 2007): 833–54. http://dx.doi.org/10.1198/106186007x256080.

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36

Mees, A. I., P. E. Rapp, and L. S. Jennings. "Singular-value decomposition and embedding dimension." Physical Review A 36, no. 1 (July 1, 1987): 340–46. http://dx.doi.org/10.1103/physreva.36.340.

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37

DANAHER, S., and E. O'MONGAIN. "Singular value decomposition in multispectral radiometry." International Journal of Remote Sensing 13, no. 9 (June 1992): 1771–77. http://dx.doi.org/10.1080/01431169208904226.

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38

Clark, C., and A. F. Clark. "Spectral identification by singular value decomposition." International Journal of Remote Sensing 19, no. 12 (January 1998): 2317–29. http://dx.doi.org/10.1080/014311698214749.

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39

Alahmadi, Adel, S. K. Jain, and André Leroy. "Decomposition of singular matrices into idempotents." Linear and Multilinear Algebra 62, no. 1 (January 23, 2013): 13–27. http://dx.doi.org/10.1080/03081087.2012.754439.

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40

Henningsson, Rasmus, and Magnus Fontes. "SMSSVD: SubMatrix Selection Singular Value Decomposition." Bioinformatics 35, no. 3 (July 13, 2018): 478–86. http://dx.doi.org/10.1093/bioinformatics/bty566.

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41

Raghavendar, Jajimogga, and V. Dhar maiah. "Singular Value Decomposition & Few Application." International Journal of Mathematics Trends and Technology 49, no. 2 (September 25, 2017): 138–42. http://dx.doi.org/10.14445/22315373/ijmtt-v49p517.

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42

P, Gowri, Senbaga Priya K, Hari Prasath R K, and Pavithra S. "Image Compression Using Singular Value Decomposition." International Journal of Mathematics Trends and Technology 67, no. 8 (August 25, 2019): 74–81. http://dx.doi.org/10.14445/22315373/ijmtt-v65i8p507.

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43

Shah, Mili I., and Danny C. Sorensen. "A Symmetry Preserving Singular Value Decomposition." SIAM Journal on Matrix Analysis and Applications 28, no. 3 (January 2006): 749–69. http://dx.doi.org/10.1137/050646676.

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44

de Franco, Roberto, and Gemma Musacchio. "Polarization filter with singular value decomposition." GEOPHYSICS 66, no. 3 (May 2001): 932–38. http://dx.doi.org/10.1190/1.1444983.

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We present a singular value decomposition (SVD) based algorithm for polarization filtering of triaxial seismic recordings based on the assumption that the particle motion trajectory is essentially 2-D (elliptical polarization). The filter is the sum of the first two eigenimages of the SVD on the signal matrix. Weighing functions, which are strictly dependent on the intensity (linearity and planarity) of the polarization, are applied. The efficiency of the filter is tested on synthetic traces and on real data, and found to be superior to solely covariance‐based filter algorithms. Although SVD and covariance‐based methods have similar theoretical approach to the solution of the eigenvalue problem, SVD does not require any further rotation along the polarization ellipsoid principal axes. The algorithm presented here is a robust and fast filter that properly reproduces polarization attributes, amplitude, and phase of the original signal. A major novelty is the enhancement of both elliptical and linear polarized signals. Moreover as SVD preserves the amplitude ratios across the triaxial recordings, the particle motion ellipse before and after filtering retains a correct orientation, overcoming a typical artifact of the covariance‐based methods.

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45

Cichocki, A. "Neural network for singular value decomposition." Electronics Letters 28, no. 8 (1992): 784. http://dx.doi.org/10.1049/el:19920495.

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46

He, Yanmin, Tao Gan, Wufan Chen, and Houjun Wang. "Adaptive Denoising by Singular Value Decomposition." IEEE Signal Processing Letters 18, no. 4 (April 2011): 215–18. http://dx.doi.org/10.1109/lsp.2011.2109039.

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47

Swathi, H. R., Shah Sohini, Surbhi, and G. Gopichand. "Image compression using singular value decomposition." IOP Conference Series: Materials Science and Engineering 263 (November 2017): 042082. http://dx.doi.org/10.1088/1757-899x/263/4/042082.

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48

Greenacre, Michael. "Singular value decomposition of matched matrices." Journal of Applied Statistics 30, no. 10 (December 2003): 1101–13. http://dx.doi.org/10.1080/0266476032000107132.

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49

Wang, Shih-Ho, T. F. Lee, and R. Zachery. "System identification via singular value decomposition." Electronics Letters 32, no. 1 (1996): 76. http://dx.doi.org/10.1049/el:19960030.

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50

Jidigam, Ranjith Kumar, Thomas H. Austin, and Mark Stamp. "Singular value decomposition and metamorphic detection." Journal of Computer Virology and Hacking Techniques 11, no. 4 (July 24, 2014): 203–16. http://dx.doi.org/10.1007/s11416-014-0220-0.

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