Geodesic
On circuit inclusion sets for the singular values of a square matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 78-93 
L. Yu. Kolotilina. On circuit inclusion sets for the singular values of a square matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 78-93. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a7/
@article{ZNSL_2008_359_a7,
     author = {L. Yu. Kolotilina},
     title = {On circuit inclusion sets for the singular values of a~square matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {78--93},
     year = {2008},
     volume = {359},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper considers different circuit inclusion sets for the singular values of a square matrix. It is shown that in both the general and structurally symmetric cases, the circuit inclusion sets are of theoretical interest only, because they coincide with much simpler Ostrowski–Brauer type inclusion sets, which should be used in practice. Bibl. – 10 titles.

[1] L. Yu. Kolotilina, “Problema vyrozhdennosti/nevyrozhdennosti dlya matrits, udovletvoryayuschikh usloviyam diagonalnogo preobladaniya, formuliruemym v terminakh orientirovannykh grafov”, Zap. nauchn. semin. POMI, 309, POMI, SPb., 2004, 40–83 | MR | Zbl

[2] L. Yu. Kolotilina, “Mnozhestva, soderzhaschie singulyarnyi spektr kvadratnoi matritsy”, Zap. nauchn. semin. POMI, 359, POMI, SPb., 2008, 52–77 | MR

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[4] H.-B. Li, T.-Z. Huang, H. Li, “Inclusion sets for singular values”, Linear Algebra Appl., 428 (2008), 2220–2235 | DOI | MR | Zbl

[5] H.-B. Li, T.-Z. Huang, H. Li, S.-Q. Shen, “Optimal Gerschgorin-type inclusion intervals of singular values”, Numer. Linear Algebra Appl., 14 (2007), 115–128 | DOI | MR | Zbl

[6] J. S. Li, K. Yang, Q.-X. Wang, “Digraphs and inclusion intervals of Brualdi-type for singular values”, Acta Math. Appl. Sin., 18 (2002), 471–476 | DOI | MR | Zbl

[7] L. Li, “The undirected graph and estimates of matrix singular values”, Linear Algebra Appl., 285 (1998), 181–188 | DOI | MR | Zbl

[8] L. L. Li, “Estimation of matrix singular values”, Comput. Math. Appl., 37 (1999), 9–15 | MR

[9] W. Li, Q. Chang, “Inclusion intervals of singular values and applications”, Comput. Math. Appl., 45 (2003), 1637–1646 | DOI | MR | Zbl

[10] L. Qi, “Some simple estimates for singular values of a matrix”, Linear Algebra Appl., 56 (1984), 105–119 | DOI | MR | Zbl