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Journals / Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi / 1996 / Cilt: 9 Sayı: 1

A Tutorial On The Singular Value Decomposition

Abdurrahman KARAMANCIOĞLU
Can ÖZDEMİR
Pages
1–12
Publication Date
1996-06-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also presenî a numerical viewpointfor SVD m orcfer to keep the maîerial setf-contained. in the last section we îreat a special problemwhere action ofîhe matrix A is restncted to a gıven subspace.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An m y, n real matm A can be factored as ITWV , where V and V areorthonormal, and W is upper left diagonal.
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Key Findings & Data:Thîs factorization is called Singular VaîueDecomposilion (SVD).
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Conclusion & Impact:We also presenî a numerical viewpointfor SVD m orcfer to keep the maîerial setf-contained. in the last section we îreat a special problemwhere action ofîhe matrix A is restncted to a gıven subspace.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Singular values · matrix decomposition · matrix

Abstract

An m y, n real matm A can be factored as ITWV , where V and V areorthonormal, and W is upper left diagonal. Thîs factorization is called Singular VaîueDecomposilion (SVD). The matrlces U, W, and V are usefül in characterizing ıhe malrix A. inthis manuscript geometric characterizations are emphasized. Geometric characîerizations areanaîyzed in terms ofsubspaces, matrix scaling, cmd norms. We also presenî a numerical viewpointfor SVD m orcfer to keep the maîerial setf-contained. in the last section we îreat a special problemwhere action ofîhe matrix A is restncted to a gıven subspace.

Özet

An m y, n real matm A can be factored as ITWV , where V and V are

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Cite This Article

KARAMANCIOĞLU, A., ÖZDEMİR, C. (1996). A Tutorial On The Singular Value Decomposition. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, Cilt: 9 Sayı: 1, 1–12. https://ajindex.com/articles/905278

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References (10)

  1. F. M. Caliler and C. A. Desoer, Multıvariahle Feedback Systems, Springcr-Verlag, 1982
  2. D, S. Watkins, Fundamenlals ofMalm Compulalions, John Wiley and Sons, 1991. [3]C.L. La.wsonandR, J. Haııson, Ao;vın^/, eaî(Sîuares7'ro6/ems, Prentice-Hall, 1974
  3. G, W. Stewart, Inlroduclion loMatrjx Computalions, Academic Press, 1973, [5] V. C. Klema and A. J. Laub, "The singular value decomposition; Its computation and some applications, " IEEE Trans. Aulomal. Contr., vo\. 25, pp. 164-176, Apr. 1980
  4. M. G. Safonov, A. J. Laub and G. L. Hartmann, "Feedback properties ofmultivariable systems: The röle and use ofthe retum difîerence matrix, " IEEE Trans. Automat. Contr., vol. 26, pp. 47-65, Febr. 1981
  5. N A. Lehtomaki, N. R. Sandell and M. Athans, "Robustness results in linear-quadratic gaussian based multivariable control design/'/££'£'7/'ö/îA'. Autöma/. Con//'., vol. 26, pp. 75-92, Febr. 1981, [8] J. Vandewalîc and B. D. Moore, "On the use of singular value decomposition in identification and signal processing, " Numericaî Linear Algehra, Digıtaî Ssgnal Processing and Paralîel Algorithms, Edited by G. H. Golub and P. Van Dooren, Springer-Verlag, 1991
  6. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, Cambridge Unİv. Press, 1991
  7. J. G. F. Francis, "The QR transformation I, " Compııler Journal, pp. 265-271, 1961
  8. J. G. F. Francis, "The QR transformation II, " CompulerJournal, pp. 332-345, 1962
  9. J. H. Witkinson, The algebraic esgenvalue problem, CIarendon Press, Oxford, 1965
  10. J. P. Chariier, M. Vanbegin, and P. Van Dooren, "On effıcienl implimentation of Kogbetliantz's algorithm for computmg singular value dccomposition, " Numerische Mathematik, pp. 279-300, 1988.