Geodesic
Diagonal dominance characterization of $PM$- and $PH$-matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXII, Tome 367 (2009), pp. 110-120 
L. Yu. Kolotilina. Diagonal dominance characterization of $PM$- and $PH$-matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXII, Tome 367 (2009), pp. 110-120. http://geodesic.mathdoc.fr/item/ZNSL_2009_367_a7/
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     author = {L. Yu. Kolotilina},
     title = {Diagonal dominance characterization of $PM$- and $PH$-matrices},
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     year = {2009},
     volume = {367},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_367_a7/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

New characterizations of the so-called $PM$- and $PH$-matrices in terms of generalized diagonal dominance are obtained and used to derive some of their properties. Also it is proved that a $PH$-matrix necessarily has a certain number of strictly diagonally dominant rows. Bibl. – 8 titles.

[1] L. Yu. Kolotilina, “Ob uluchshenii otsenok Chistyakova dlya perronovskogo kornya neotritsatelnoi matritsy”, Zap. nauchn. semin. POMI, 346, 2007, 103–118 | MR

[2] L. Yu. Kolotilina, “Otsenki obratnykh dlya $PM$- i $PH$-matrits”, Zap. nauchn. semin. POMI, 367, 2009, 75–109 | MR

[3] A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York etc., 1979 | MR | Zbl

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

[5] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991 | MR | Zbl

[6] L. Yu. Kolotilina, “Bounds for the infinity norm of the inverse for certain $M$- and $H$-matrices”, Linear Algebra Appl., 430 (2009), 692–702 | DOI | MR | Zbl

[7] H. Minc, Nonnegative Matrices, John Wiley Sons, New York etc., 1964 | MR

[8] R. S. Varga, Geršgorin and His Circles, Springer, 2004 | MR