Quadratic matrix polynomials with a parameter

DOI10.1016/0196-8858(86)90036-9zbMath0623.15003OpenAlexW2000031927MaRDI QIDQ1091445

Israel Gohberg, Peter Lancaster, Leiba Rodman

Publication date: 1986

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0196-8858(86)90036-9

zbMATH Keywords

generalized eigenvaluesmatrix polynomialdamped vibrating systems

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Linear ordinary differential equations and systems (34A30) Stability for problems in linear vibration theory (70J25) Matrix pencils (15A22)

Related Items

Matrix measures, moment spaces and Favard's theorem for the interval \([0,1\) and \([0,\infty)\)], Algorithms for hyperbolic quadratic eigenvalue problems, Coupling homogeneous chains of damped harmonic oscillators, Use of indefinite pencils for computing damped natural modes, Remarks on the perturbation of analytic matrix functions. III, Semidefinite perturbations of analytic Hermitian matrix functions, On linear vibrational systems with one dimensional damping. II, A Systematic Analysis on Analyticity of Semisimple Eigenvalues of Matrix-Valued Functions, Sensitivity analysis of semi-simple eigenvalues of regular quadratic eigenvalue problems

Cites Work

• Matrices and indefinite scalar products
• Analytic perturbation theory for matrices and operators. Licensed ed
• Spectral analysis of selfadjoint matrix polynomials
• Analytic matrix functions with prescribed local data
• A fundamental theorem on lambda-matrices with applications. I: Ordinary differential equations with constant coefficients
• On some mathematical principles in the linear theory of damped oscillations of continua II
• Perturbations of H-selfadjoint matrices, with applications to differential equations
• Stability of invariant maximal semidefinite subspaces. I
• Perturbation of analytic hermitian matrix functions
• Perturbation Theory for Divisors of Operator Polynomials
• A sign characteristic for selfadjoint meromorphic matrix functions
• Common multiples and common divisors of matrix polynomials, II. Vandermonde and resultant matrices
• On the Problem of Runs
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