Homotopy method for generalized eigenvalue problems \(Ax=\lambda Bx\)

DOI10.1016/0024-3795(87)90060-7zbMath0621.65028OpenAlexW2023512872MaRDI QIDQ1090068

Tien-Yien Li, Timothy Sauer

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90060-7

zbMATH Keywords

eigensolutionalgebraic eigenvalue problemHomotopy methods

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items

Optimal homotopy methods for solving nonlinear systems. I: Nonsingular homotopy paths, Solving polynomial systems, A note on the homotopy method for linear algebraic eigenvalue problems, A simple homotopy for solving deficient polynomial systems, The random product homotopy and deficient polynomial systems, The globalization of Durand-Kerner algorithm, Complexity of path-following methods for the eigenvalue problem, Numerical pulsrodons of the \((2+1)\)-dimensional rotating shallow water system, On the general boundary element method, On affine scaling algorithms for nonconvex quadratic programming, A homotopy algorithm for a symmetric generalized eigenproblem, Probabilistic analyses of condition numbers, Homotopy-Determinant Algorithm for Solving Nonsymmetric Eigenvalue Problems, Numerical complexiton solutions for the complex KdV equation by the homotopy perturbation method, The continuation method for rational and deficient systems, An approximate solution treatment for nonlinear problems, A randomized homotopy for the Hermitian eigenpair problem, Structure variable homotopy methods for solving nonlinear systems

Uses Software

• HOMPACK

Cites Work

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• A homotopy for solving polynomial systems
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• Numerical Solution of a Class of Deficient Polynomial Systems
• Algorithm 652
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• On the Number of Solutions to Polynomial Systems of Equations
• Determining All Solutions to Certain Systems of Nonlinear Equations
• Finding all solutions to polynomial systems and other systems of equations