Relevant bibliographies by topics / Singular decomposition

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Singular decomposition'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Singular decomposition"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Singular decomposition"

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Ek, Christoffer. "Singular Value Decomposition." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-21481.

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Digital information och kommunikation genom digitala medier är ett växande område. E-post och andra kommunikationsmedel används dagligen över hela världen. Parallellt med att området växer så växer även intresset av att hålla informationen säker. Transmission via antenner är inom signalbehandling ett välkänt område. Transmission från en sändare till en mottagare genom fri rymd är ett vanligt exempel. I en tuff miljö som till exempel ett rum med reflektioner och oberoende elektriska apparater kommer det att finnas en hel del distorsion i systemet och signalen som överförs kan, på grund av systemets egenskaper och buller förvrängas.Systemidentifiering är ett annat välkänt begrepp inom signalbehandling. Denna avhandling fokuserar på systemidentifiering i en tuff miljö med okända system. En presentation ges av matematiska verktyg från den linjära algebran samt en tillämpning inom signalbehandling. Denna avhandling grundar sig främst på en matrisfaktorisering känd som Singular Value Decomposition (SVD). SVD’n används här för att lösa komplicerade matrisinverser och identifiera system.Denna avhandling utförs i samarbete med Combitech AB. Deras expertis inom signalbehandling var till stor hjälp när teorin praktiserades. Med hjälp av ett välkänt programmeringsspråk känt som LabView praktiserades de matematiska verktygen och kunde synkroniseras med diverse instrument som användes för att generera signaler och system.
Digital information transmission is a growing field. Emails, videos and so on are transmitting around the world on a daily basis. Along the growth of using digital devises there is in some cases a great interest of keeping this information secure. In the field of signal processing a general concept is antenna transmission. Free space between an antenna transmitter and a receiver is an example of a system. In a rough environment such as a room with reflections and independent electrical devices there will be a lot of distortion in the system and the signal that is transmitted might, due to the system characteristics and noise be distorted. System identification is another well-known concept in signal processing. This thesis will focus on system identification in a rough environment and unknown systems. It will introduce mathematical tools from the field of linear algebra and applying them in signal processing. Mainly this thesis focus on a specific matrix factorization called Singular Value Decomposition (SVD). This is used to solve complicated inverses and identifying systems. This thesis is formed and accomplished in collaboration with Combitech AB. Their expertise in the field of signal processing was of great help when putting the algorithm in practice. Using a well-known programming script called LabView the mathematical tools were synchronized with the instruments that were used to generate the systems and signals.
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Kwizera, Petero. "Matrix Singular Value Decomposition." UNF Digital Commons, 2010. http://digitalcommons.unf.edu/etd/381.

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This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations.
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Samuelsson, Saga. "The Singular Value Decomposition Theorem." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-150917.

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This essay will present a self-contained exposition of the singular value decomposition theorem for linear transformations. An immediate consequence is the singular value decomposition for complex matrices.
Denna uppsats kommer presentera en självständig exposition av singulärvärdesuppdelningssatsen för linjära transformationer. En direkt följd är singulärvärdesuppdelning för komplexa matriser.
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Jolly, Vineet Kumar. "Activity Recognition using Singular Value Decomposition." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/35219.

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A wearable device that accurately records a user's daily activities is of substantial value. It can be used to enhance medical monitoring by maintaining a diary that lists what a person was doing and for how long. The design of a wearable system to record context such as activity recognition is influenced by a combination of variables. A flexible yet systematic approach for building a software classification environment according to a set of variables is described. The integral part of the software design is the use of a unique robust classifier that uses principal component analysis (PCA) through singular value decomposition (SVD) to perform real-time activity recognition. The thesis describes the different facets of the SVD-based approach and how the classifier inputs can be modified to better differentiate between activities. This thesis presents the design and implementation of a classification environment used to perform activity detection for a wearable e-textile system.
Master of Science
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Khatavkar, Rohan. "Sparse and orthogonal singular value decomposition." Kansas State University, 2013. http://hdl.handle.net/2097/15992.

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Master of Science
Department of Statistics
Kun Chen
The singular value decomposition (SVD) is a commonly used matrix factorization technique in statistics, and it is very e ective in revealing many low-dimensional structures in a noisy data matrix or a coe cient matrix of a statistical model. In particular, it is often desirable to obtain a sparse SVD, i.e., only a few singular values are nonzero and their corresponding left and right singular vectors are also sparse. However, in several existing methods for sparse SVD estimation, the exact orthogonality among the singular vectors are often sacri ced due to the di culty in incorporating the non-convex orthogonality constraint in sparse estimation. Imposing orthogonality in addition to sparsity, albeit di cult, can be critical in restricting and guiding the search of the sparsity pattern and facilitating model interpretation. Combining the ideas of penalized regression and Bregman iterative methods, we propose two methods that strive to achieve the dual goal of sparse and orthogonal SVD estimation, in the general framework of high dimensional multivariate regression. We set up simulation studies to demonstrate the e cacy of the proposed methods.
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Kardamis, Joseph R. "Audio watermarking techniques using singular value decomposition /." Online version of thesis, 2007. http://hdl.handle.net/1850/4493.

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Montagnon, Chris. "Singular value decomposition and time series forecasting." Thesis, Imperial College London, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535012.

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Rajamanickam, Sivasankaran. "Efficient algorithms for sparse singular value decomposition." [Gainesville, Fla.] : University of Florida, 2009. http://purl.fcla.edu/fcla/etd/UFE0041153.

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Deng, Cheng. "Time Series Decomposition Using Singular Spectrum Analysis." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2352.

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Singular Spectrum Analysis (SSA) is a method for decomposing and forecasting time series that recently has had major developments but it is not yet routinely included in introductory time series courses. An international conference on the topic was held in Beijing in 2012. The basic SSA method decomposes a time series into trend, seasonal component and noise. However there are other more advanced extensions and applications of the method such as change-point detection or the treatment of multivariate time series. The purpose of this work is to understand the basic SSA method through its application to the monthly average sea temperature in a point of the coast of South America, near where “EI Ni˜no” phenomenon originates, and to artificial time series simulated using harmonic functions. The output of the basic SSA method is then compared with that of other decomposition methods such as classic seasonal decomposition, X-11 decomposition using moving averages and seasonal decomposition by Loess (STL) that are included in some time series courses.
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Ho, Anna. "Cross sentence alignment based on singular value decomposition." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1942865.

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Books on the topic "Singular decomposition"

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Deift, Percy. The bidiagonal singular value decomposition and Hamiltonian mechanics. New York: Courant Institute of Mathematical Sciences, New York University, 1989.

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Kei, Takeuchi, Takane Yoshio, and SpringerLink (Online service), eds. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. New York, NY: Springer Science+Business Media, LLC, 2011.

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Yanai, Haruo, Kei Takeuchi, and Yoshio Takane. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9887-3.

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Dhar, Pranab Kumar, and Tetsuya Shimamura. Advances in Audio Watermarking Based on Singular Value Decomposition. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14800-7.

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Gilsinn, David. Updating a turning center error model by singular value decomposition. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 2001.

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Elsner, James B. Singular spectrum analysis: A new tool in time series analysis. New York: Plenum Press, 1996.

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Sen, sujit. Innovations and singular value decomposition for blind sequence detection in wireless channels. Ottawa: National Library of Canada, 1999.

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Torres, Rodolfo H. Boundedness results for operators with singular kernels on distribution spaces. Providence, R.I., USA: American Mathematical Society, 1991.

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Yao, Kung. Final report to NASA-Ames Research Center, Moffett Field, CA 94034, contract no. NAG 2-433, January 1, 1987 - March 31, 1988 on efficient load measurements using singular value decomposition. Los Angeles, CA: Laboratory for Flight Systems Research, University of California, 1989.

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Yao, Kung. Final report to NASA-Ames Research Center, Moffett Field, CA 94034, contract no. NAG 2-433, January 1, 1987 - March 31, 1988 on efficient load measurements using singular value decomposition. Los Angeles, CA: Laboratory for Flight Systems Research, University of California, 1989.

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Book chapters on the topic "Singular decomposition"

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Aggarwal, Charu C. "Singular Value Decomposition." In Linear Algebra and Optimization for Machine Learning, 299–337. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40344-7_7.

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Kanatani, Kenichi. "Singular Value Decomposition." In Computer Vision, 1–4. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-03243-2_802-1.

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Brown, Jonathon D. "Singular Value Decomposition." In Advanced Statistics for the Behavioral Sciences, 149–86. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93549-2_5.

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Zhang, Yanchun, and Guandong Xu. "Singular Value Decomposition." In Encyclopedia of Database Systems, 3506–8. New York, NY: Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4614-8265-9_538.

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Zhang, Yanchun, and Guandong Xu. "Singular Value Decomposition." In Encyclopedia of Database Systems, 2657–58. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-39940-9_538.

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Puntanen, Simo, George P. H. Styan, and Jarkko Isotalo. "Singular Value Decomposition." In Matrix Tricks for Linear Statistical Models, 391–414. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10473-2_20.

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Lange, Kenneth. "Singular Value Decomposition." In Numerical Analysis for Statisticians, 129–42. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-5945-4_9.

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Zhang, Yanchun, and Guandong Xu. "Singular Value Decomposition." In Encyclopedia of Database Systems, 1–3. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4899-7993-3_538-2.

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Helmke, Uwe, and John B. Moore. "Singular Value Decomposition." In Communications and Control Engineering, 81–100. London: Springer London, 1994. http://dx.doi.org/10.1007/978-1-4471-3467-1_3.

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Godunov, S. K., A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin. "Singular Value Decomposition." In Guaranteed Accuracy in Numerical Linear Algebra, 1–108. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1952-8_1.

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Conference papers on the topic "Singular decomposition"

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"Material decomposition using a singular value decomposition method." In 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC). IEEE, 2013. http://dx.doi.org/10.1109/nssmic.2013.6829379.

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Le Bihan, N. "Color image decomposition using quaternion singular value decomposition." In International Conference on Visual Information Engineering (VIE 2003). Ideas, Applications, Experience. IEE, 2003. http://dx.doi.org/10.1049/cp:20030500.

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Sekmen, Ali, Akram Aldroubi, Ahmet Bugra Koku, and Keaton Hamm. "Matrix resconstruction: Skeleton decomposition versus singular value decomposition." In 2017 International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS). IEEE, 2017. http://dx.doi.org/10.23919/spects.2017.8046777.

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Han, Shuguo, Wee Keong Ng, and Philip S. Yu. "Privacy-Preserving Singular Value Decomposition." In 2009 IEEE 25th International Conference on Data Engineering (ICDE). IEEE, 2009. http://dx.doi.org/10.1109/icde.2009.217.

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Pilgram, Schappacher, and Pfurtscheller. "Method Using Singular Value Decomposition." In Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 1992. http://dx.doi.org/10.1109/iembs.1992.592988.

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Mistry, Nirav, Sudeep Tanwar, Sudhanshu Tyagi, and Pradeep Kr Singh. "Tensor Decomposition of Biometric Data using Singular Value Decomposition." In 2018 Fifth International Conference on Parallel, Distributed and Grid Computing (PDGC). IEEE, 2018. http://dx.doi.org/10.1109/pdgc.2018.8745719.

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Sugamya, Katta, Suresh Pabboju, and A. VinayaBabu. "Image enhancement using singular value decomposition." In 2016 International Conference on Research Advances in Integrated Navigation Systems (RAINS). IEEE, 2016. http://dx.doi.org/10.1109/rains.2016.7764388.

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Hegedus, Istvan, Mark Jelasity, Levente Kocsis, and Andras A. Benczur. "Fully distributed robust singular value decomposition." In 2014 IEEE Thirteenth International Conference on Peer-to-Peer Computing (P2P). IEEE, 2014. http://dx.doi.org/10.1109/p2p.2014.6934299.

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Hou, Junhui, Jie Chen, Lap-Pui Chau, and Ying He. "Sparse two-dimensional singular value decomposition." In 2016 IEEE International Conference on Multimedia and Expo (ICME). IEEE, 2016. http://dx.doi.org/10.1109/icme.2016.7552922.

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H. Fan, Michael K., and Andre L. Tits. "Toward a structure singular value decomposition." In 26th IEEE Conference on Decision and Control. IEEE, 1987. http://dx.doi.org/10.1109/cdc.1987.272766.

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Reports on the topic "Singular decomposition"

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Luk, Franklin T. Deconvolution and Singular Value Decomposition. Fort Belvoir, VA: Defense Technical Information Center, November 1994. http://dx.doi.org/10.21236/ada286582.

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Miller, Timothy C., and Ravinder Chona. Overdeterministic Fracture Analysis and Singular Value Decomposition. Fort Belvoir, VA: Defense Technical Information Center, April 1999. http://dx.doi.org/10.21236/ada409496.

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Fahnline, JB, RL Campbell, and SA Hambric. Modal Analysis Using the Singular Value Decomposition. Office of Scientific and Technical Information (OSTI), February 2004. http://dx.doi.org/10.2172/836294.

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Miller, Timothy C., and Ravinder Chona. Overdeterministic Fracture Analysis and Singular Value Decomposition. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada386847.

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Bro, Rasmus, Evrim Acar, and Tamara Gibson Kolda. Resolving the sign ambiguity in the singular value decomposition. Office of Scientific and Technical Information (OSTI), October 2007. http://dx.doi.org/10.2172/920802.

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Rust, Bert W. Truncating the singular value decomposition for ILL-posed problems. Gaithersburg, MD: National Institute of Standards and Technology, 1998. http://dx.doi.org/10.6028/nist.ir.6131.

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Gilsinn, David E., Herbert T. Brandy, and Alice V. Ling. Updating a turning center error model by singular value decomposition. Gaithersburg, MD: National Institute of Standards and Technology, 2001. http://dx.doi.org/10.6028/nist.ir.6722.

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Hoff, Peter D. Model Averaging and Dimension Selection for the Singular Value Decomposition. Fort Belvoir, VA: Defense Technical Information Center, January 2006. http://dx.doi.org/10.21236/ada454966.

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Kim, J. S. Data analysis of tokamak experiments with singular value decomposition. Final report. Office of Scientific and Technical Information (OSTI), April 1997. http://dx.doi.org/10.2172/555486.

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Chu, Nhi-Anh. An Implementation of the Singular Value Decomposition on the Connection Machine CM-2. Fort Belvoir, VA: Defense Technical Information Center, April 1991. http://dx.doi.org/10.21236/ada234124.

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