Summary
By using Gershgorin's theorem and the theorems on minimal Gershgorin disks a posteriori error bounds for the zeros of a polynomial are deduced, from which the bounds given in [1] by Braess and Hadeler are easily obtained.
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References
Braess, D., Hadeler, K. P.: Simultaneous inclusion of the zeros of a polynomial. Numer. Math.21, 161–165 (1973)
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Elsner, L.: Über Eigenwerteinschließungen mit Hilfe von Gershgorinkreisen. ZAMM50, 381–384 (1970)
Medley, H. S., Varga, R. S.: On smallest isolated Gershgorin discs for eigenvalues. II. Numer. Math.11, 320–323 (1968)
Smith, B. T.: Error bounds for the zeros of a polynomial based upon Gershgorin's theorem. JACM17, 661–674 (1970)
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Elsner, L. A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem. Numer. Math. 21, 425–427 (1973). https://doi.org/10.1007/BF01436492
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DOI: https://doi.org/10.1007/BF01436492