Araştırma Makalesi
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A Tutorial On The Singular Value Decomposition

Yıl 1996, Cilt: 9 Sayı: 1, 1 - 12, 30.06.1996

Abdurrahman Karamancıoğlu Can Özdemir

Öz

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

Anahtar Kelimeler

Singular values matrix decomposition matrix

Kaynakça

  • [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.
  • [4] 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.
  • [6] 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.
  • [7] 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.
  • [9] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, Cambridge Unİv. Press, 1991.
  • [10] J. G. F. Francis, "The QR transformation I, " Compııler Journal, pp. 265-271, 1961.
  • [11] J. G. F. Francis, "The QR transformation II, " CompulerJournal, pp. 332-345, 1962.
  • [12] J. H. Witkinson, The algebraic esgenvalue problem, CIarendon Press, Oxford, 1965.
  • [13] 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.

A Tutorial On The Singular Value Decomposition

Yıl 1996, Cilt: 9 Sayı: 1, 1 - 12, 30.06.1996

Abdurrahman Karamancıoğlu Can Özdemir

Öz

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

orthonormal, and W is upper left diagonal. Thîs factorization is called Singular Vaîue

Decomposilion (SVD). The matrlces U, W, and V are usefül in characterizing ıhe malrix A. in

this manuscript geometric characterizations are emphasized. Geometric characîerizations are

anaîyzed in terms ofsubspaces, matrix scaling, cmd norms. We also presenî a numerical viewpoint

for SVD m orcfer to keep the maîerial setf-contained. in the last section we îreat a special problem

where action ofîhe matrix A is restncted to a gıven subspace.

Anahtar Kelimeler

Singular values matrix decomposition matrix

Kaynakça

  • [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.
  • [4] 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.
  • [6] 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.
  • [7] 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.
  • [9] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, Cambridge Unİv. Press, 1991.
  • [10] J. G. F. Francis, "The QR transformation I, " Compııler Journal, pp. 265-271, 1961.
  • [11] J. G. F. Francis, "The QR transformation II, " CompulerJournal, pp. 332-345, 1962.
  • [12] J. H. Witkinson, The algebraic esgenvalue problem, CIarendon Press, Oxford, 1965.
  • [13] 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Konular Elektrik Mühendisliği
Bölüm Araştırma Makaleleri
Yazarlar

Abdurrahman Karamancıoğlu

Can Özdemir Bu kişi benim

Yayımlanma Tarihi 30 Haziran 1996
Kabul Tarihi 1 Ocak 1996
Yayımlandığı Sayı Yıl 1996 Cilt: 9 Sayı: 1

Kaynak Göster

APA Karamancıoğlu, A., & Özdemir, C. (1996). A Tutorial On The Singular Value Decomposition. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, 9(1), 1-12.
AMA Karamancıoğlu A, Özdemir C. A Tutorial On The Singular Value Decomposition. ESOGÜ Müh Mim Fak Derg. Haziran 1996;9(1):1-12.
Chicago Karamancıoğlu, Abdurrahman, ve Can Özdemir. “A Tutorial On The Singular Value Decomposition”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi 9, sy. 1 (Haziran 1996): 1-12.
EndNote Karamancıoğlu A, Özdemir C (01 Haziran 1996) A Tutorial On The Singular Value Decomposition. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 9 1 1–12.
IEEE A. Karamancıoğlu ve C. Özdemir, “A Tutorial On The Singular Value Decomposition”, ESOGÜ Müh Mim Fak Derg, c. 9, sy. 1, ss. 1–12, 1996.
ISNAD Karamancıoğlu, Abdurrahman - Özdemir, Can. “A Tutorial On The Singular Value Decomposition”. Eskişehir Osmangazi Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi 9/1 (Haziran 1996), 1-12.
JAMA Karamancıoğlu A, Özdemir C. A Tutorial On The Singular Value Decomposition. ESOGÜ Müh Mim Fak Derg. 1996;9:1–12.
MLA Karamancıoğlu, Abdurrahman ve Can Özdemir. “A Tutorial On The Singular Value Decomposition”. Eskişehir Osmangazi Üniversitesi Mühendislik Ve Mimarlık Fakültesi Dergisi, c. 9, sy. 1, 1996, ss. 1-12.
Vancouver Karamancıoğlu A, Özdemir C. A Tutorial On The Singular Value Decomposition. ESOGÜ Müh Mim Fak Derg. 1996;9(1):1-12.
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