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On lower bounds for the largest eigenvalue of a symmetric matrix. (English) Zbl 1153.15311

Summary: We consider lower bounds for the largest eigenvalue of a symmetric matrix. In particular we extend a recent approach by P. Van Mieghem [Linear Algebra Appl. 427, No. 1, 119–129 (2007; Zbl 1152.15021)].

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
30B10 Power series (including lacunary series) in one complex variable

Citations:

Zbl 1152.15021
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References:

[1] Liu, X-Q.; Huang, T-Z.; Fu, Y-D., A note on improvements on bounds for nonmaximal eigenvalues of symmetric positive matrices, Linear algebra appl., 419, 612-617, (2006) · Zbl 1151.15305
[2] Van Mieghem, P., A new type of lower bound for the largest eigenvalue of a symmetric matrix, Linear algebra appl., 427, 119-129, (2007) · Zbl 1152.15021
[3] Walker, S.G., On recent Cheeger type bounds for non-maximal eigenvalues applied to positive matrices, SIAM J. matrix anal. appl., 25, 574-581, (2003) · Zbl 1057.15024
[4] Walker, S.G., Improving bounds for nonmaximal eigenvalues of nonnegative matrices, Linear algebra appl., 397, 133-139, (2005) · Zbl 1074.15027
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