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Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. (English) Zbl 1018.65049
New comparison theorems are presented for the spectral radii of matrices arising from splitting of different matrices under nonnegativity assumptions. Strict inequalities of the spectral radii are obtained without imposing strict inequalities of the matrices, and in addition new results are presented for nonstrict inequalities of the spectral radii. Combinatorical and analytic approaches are used and counter examples show that some conditions cannot be relaxed.
MSC:
65F10Iterative methods for linear systems
15A42Inequalities involving eigenvalues and eigenvectors
15A48Positive matrices and their generalizations (MSC2000)