An accelerated cyclic-reduction-based solvent method for solving quadratic eigenvalue problem of gyroscopic systems

DOI10.1016/j.camwa.2018.12.040zbMath1442.65055OpenAlexW2913166105WikidataQ128591203 ScholiaQ128591203MaRDI QIDQ2203951

Cai-Rong Chen, Chang-Feng Ma

Publication date: 2 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.12.040

zbMATH Keywords

nonlinear matrix equationquadratic eigenvalue problemcyclic reductiondoubling algorithmgyroscopic systemsolvent method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24)

Related Items (1)

GENERALIZED QUADRATIC SPECTRUM APPROXIMATION IN BOUNDED AND UNBOUNDED CASES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + \sum_{i = 1}^m A_i^\ast X^{- t_i} A_i = Q\)
• Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations
• Existence and multiplicity results for nonlinear periodic boundary value problems
• An efficient algorithm based on Lanczos type of BCR to solve constrained quadratic inverse eigenvalue problems
• The time-periodic solutions to the modified Zakharov equations with a quantum correction
• Stability of periodic steady-state solutions to a non-isentropic Euler-Maxwell system
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Solving constrained quadratic inverse eigenvalue problem via conjugate direction method
• Existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem
• Least squares solutions of quadratic inverse eigenvalue problem with partially bisymmetric matrices under prescribed submatrix constraints
• A new method for the bisymmetric minimum norm solution of the consistent matrix equations \(A_1XB_1 = C_1\), \(A_2XB_2 = C_2\)
• Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
• Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils
• The Quadratic Eigenvalue Problem
• Convergence Rate of an Iterative Method for a Nonlinear Matrix Equation
• A numerical method for quadratic eigenvalue problems of gyroscopic systems
• Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case
• Overdamped and Gyroscopic Vibrating Systems
• Strongly stable gyroscopic systems
• Iterative solution of two matrix equations
• Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
• Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations
• Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations
• Numerical solution of a quadratic eigenvalue problem

This page was built for publication: An accelerated cyclic-reduction-based solvent method for solving quadratic eigenvalue problem of gyroscopic systems