Geodesic
Pseudoblock conditions of diagonal dominance
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 94-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents new pseudoblock diagonal-dominance conditions for matrices with fixed block partitioning, which generalize the pointwise $k$th-order diagonal-dominance conditions and pointwise circuit diagonal-dominance conditions. For matrices satisfying pseudoblock conditions, the singularity/nonsingularity problem is considered. In particular, for block $2\times 2$ matrices, certain known results are improved and generalized. Some eigenvalue inclusion regions corresponding to pseudoblock nonsingularity conditions are presented. 
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     author = {L. Yu. Kolotilina},
     title = {Pseudoblock conditions of diagonal dominance},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a8/}
}
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L. Yu. Kolotilina. Pseudoblock conditions of diagonal dominance. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 94-131. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a8/

[1] L. S. Dashnits, M. S. Zusmanovich, “O nekotorykh kriteriyakh regulyarnosti matrits i lokalizatsii spektra”, Zh. vychisl. matem. matem. fiz., 10 (1970), 1092–1097 | Zbl

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

[3] A. Berman, R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1969 | MR

[4] R. Brualdi, “Matrices, eigenvalues, and directed graphs”, Linear Multilinear Algebra, 11 (1982), 143–165 | DOI | MR | Zbl

[5] L. Cvetkovic, V. Kostic, R. S. Varga, “A new Gers̆gorin-type eigenvalue inclusion set”, Electron. Trans. Numer. Anal., 18 (2004), 73–80 | MR | Zbl

[6] Y. Gao, X. Wang, “Criteria for generalized diagonally dominant matrices and $M$-matrices”, Linear Algebra Appl., 169 (1992), 257–268 | DOI | MR | Zbl

[7] F. Harary, Graph Theory, Addison–Wesley Publ. Co, 1969 | MR | Zbl

[8] T. Huang, “A note on generalized diagonally dominant matrices”, Linear Algebra Appl., 225 (1992), 237–242 | MR

[9] L. Yu. Kolotilina, “Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matrices”, Linear Algebra Appl., 359 (2003), 133–159 | DOI | MR | Zbl

[10] L. Yu. Kolotilina, “Generalizations of the Ostrowski–Brauer theorem”, Linear Algebra Appl., 364 (2003), 65–80 | DOI | MR | Zbl

[11] R. S. Varga, Gers̆gorin and His Circles, Springer Series Comput. Math., 36, Springer, 2004 | MR