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Bounds for the variation of matrix eigenvalues and polynomial roots

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/0024-3795(94)90432-4

Abstract

Abstract For two given complex matrices A, B, upper bounds are derived for the optimal matching distance between the spectra σ( A) and σ( B) in terms of ‖ A - B 2‖, where ‖ ⋅ ‖ 2 is the spectral norm. The case of arbitrary matrix norms is treated. A similar result estimates the optimal matching distance between the roots of two polynomials. These bounds replace a factor of 4 in earlier results by the value 16 (3√3) ≈3.08 .

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