On the numerical solution of nonlinear eigenvalue problems

DOI10.1007/BF02238095zbMath0828.65038OpenAlexW1548154618MaRDI QIDQ1895650

K. E. Chu, Alan L. Andrew, Peter Lancaster

Publication date: 6 December 1995

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238095

zbMATH Keywords

algorithmsNewton's methodnumerical exampleseigenvectorsnonlinear eigenvalue problemscalingmatrix equations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56)

Related Items (11)

Linear stability analysis of capillary instabilities for concentric cylindrical shells ⋮ Discrete least-squares technique for eigenvalues. I: The one-dimensional case ⋮ A method for the numerical computation of Hopf bifurcation ⋮ The nonlinear eigenvalue problem ⋮ Unnamed Item ⋮ Convergence Orders of Iterative Methods for Nonlinear Eigenvalue Problems ⋮ On a class of alternating coefficient matrices quadratic eigenvalue problem ⋮ Iterative algorithms for nonlinear ordinary differential eigenvalue problems ⋮ Photonic band structure calculations using nonlinear eigenvalue techniques ⋮ Partial derivatives of the eigen-triplet of the quadratic eigenvalue problem depending on several parameters ⋮ A survey on variational characterizations for nonlinear eigenvalue problems

Cites Work

• The generalized eigenvalue problem and acoustic surface wave computations
• A generalized Rayleigh quotient iteration for lambda-matrices
• Realistic error bounds for a simple eigenvalue and its associated eigenvector
• Algorithms for lambda-matrices
• Derivatives of Eigenvalues and Eigenvectors of Matrix Functions
• Characterization and Computation of Generalized Turning Points
• Bordered Matrices, Singular Systems, and Ergodic Markov Chains
• Deferred correction for the ordinary differential equation eigenvalue problem
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• Deferred correction for the integral equation eigenvalue problem
• Generalized Eigenvalue Problems for Rectangular Matrices
• Matrices with Rank Deficiency Two in Eigenvalue Problems and Dynamical Systems
• Some applications of the Newton—Raphson method to non-linear matrix problems
• Algorithms for the Nonlinear Eigenvalue Problem
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