Geodesic
On Ostrowski's disk theorem and lower bounds for the smallest eigenvalues and singular values
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 125-140

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The paper refines the classical Ostrowski disk theorem and suggests lower bounds for the smallest-in-modulus eigenvalue and the smallest singular value of a square matrix under certain diagonal dominance conditions. A lower bound for the smallest-in-modulus eigenvalue of a product of $m\ge2$ matrices satisfying joint diagonal dominance conditions is obtained. The particular cases of the bounds suggested that correspond to the infinity norm are discussed and compared with some known results. Bibl. 9 titles. 
@article{ZNSL_2010_382_a9,
     author = {L. Yu. Kolotilina},
     title = {On {Ostrowski's} disk theorem and lower bounds for the smallest eigenvalues and singular values},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--140},
     publisher = {mathdoc},
     volume = {382},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a9/}
}
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L. Yu. Kolotilina. On Ostrowski's disk theorem and lower bounds for the smallest eigenvalues and singular values. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 125-140. http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a9/