## Bounds of modulus of eigenvalues based on Stein equation.(English)Zbl 1205.15031

The authors study some bounds of the eigenvalue moduli of a complex matrix. The bounds are related to the Stein equation $$H-A^*HA = I$$. Sequences are constructed to estimate the upper and lower bounds for the maximum and minimum eigenvalue moduli. It is also pointed out that the sequences are not practical for computational purpose.

### MSC:

 15A42 Inequalities involving eigenvalues and eigenvectors 65F15 Numerical computation of eigenvalues and eigenvectors of matrices

### Keywords:

eigenvalues; lower and upper bounds; Stein equation

Algorithm 432
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### References:

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