Iterative methods for large continuation problems
Copyright policy )Iterative methods for large continuation problems
This is a nice summary of continuation methods for nonlinear parameter dependent problems and implicitly restarted block-Lanczos method for computation of a few eigenvalues and the associated eigenvectors of a symmetric matrix. By combining these techniques the authors developed algorithms for path following around a turning point, detecting singular points on the solution path and for branch switching at a bifurcation point. The algorithms are proposed for large continuation problems and are illustrated by numerical examples.
- Case Western Reserve University United States
- Kent State University at Salem United States
- University System of Ohio United States
- Kent State University United States
- Kent State University United States
numerical examples, symmetric matrix, Eigenvalue computation, Applied Mathematics, Numerical computation of solutions to systems of equations, eigenvectors, continuation problem, Bordering algorithm, continuation methods, algorithms, Turning point, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, turning point, Numerical solution of nonlinear eigenvalue and eigenvector problems, nonlinear parameter dependent problems, Computational Mathematics, Nonlinear system, iteration method, restarted block-Lanczos method, Bifurcation point, eigenvalue, singular point, Path following
numerical examples, symmetric matrix, Eigenvalue computation, Applied Mathematics, Numerical computation of solutions to systems of equations, eigenvectors, continuation problem, Bordering algorithm, continuation methods, algorithms, Turning point, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, turning point, Numerical solution of nonlinear eigenvalue and eigenvector problems, nonlinear parameter dependent problems, Computational Mathematics, Nonlinear system, iteration method, restarted block-Lanczos method, Bifurcation point, eigenvalue, singular point, Path following
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