Taylor expansions of eigenvalues of perturbed matrices with applications to spectral radii of nonnegative matrices

DOI10.1016/0024-3795(92)90293-JzbMath0748.15019OpenAlexW2081395081MaRDI QIDQ1189629

Moshe Haviv, Uriel G. Rothblum, Ya'acov Ritov

Publication date: 27 September 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90293-j

zbMATH Keywords

eigenvalueeigenvectorsrecursive algorithmcomplex matricesspectral radiinonnegative irreducible matricesperturbed matricesTaylor power series expansions

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items

Perron-Frobenius theory over real closed fields and fractional power series expansions ⋮ Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues ⋮ A solution of a nonlinear system arising in spectral perturbation theory of nonnegative matrices ⋮ Nonnegative alternating circulants leading to \(M\)-matrix group inverses ⋮ Some results on eigenvalues of finite type, resolvents and Riesz projections ⋮ Maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices ⋮ Perturbation of null spaces with application to the eigenvalue problem and generalized inverses ⋮ Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes ⋮ Inverting a Matrix Function around a Singularity via Local Rank Factorization ⋮ Resolvent and logarithmic residues of a singular operator pencil in Hilbert spaces

Cites Work

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• Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix
• Derivatives and Perturbations of Eigenvectors
• Derivatives of the spectral radius as a function of non-negative matrix elements