Geodesic
Bounds for eigenvalues of symmetric block Jacobi scaled matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part IX, Tome 202 (1992), pp. 18-25 
L. Yu. Kolotilina. Bounds for eigenvalues of symmetric block Jacobi scaled matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part IX, Tome 202 (1992), pp. 18-25. http://geodesic.mathdoc.fr/item/ZNSL_1992_202_a1/
@article{ZNSL_1992_202_a1,
     author = {L. Yu. Kolotilina},
     title = {Bounds for eigenvalues of symmetric block {Jacobi} scaled matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {18--25},
     year = {1992},
     volume = {202},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_202_a1/}
}
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The paper presents upper bounds for the largest eigenvalue of a block Jacobi scaled symmetric positive-definite matrix which depend only on such parameters as the block semibandwidth of a matrix and its block size. From these bounds we also derive upper bounds for the smallest eigenvalue of a symmetric matrix with identity diagonal blocks. Bibliography: 4 titles.