Global monotone convergence of Newton iteration for a nonlinear eigen-problem
Copyright policy )Global monotone convergence of Newton iteration for a nonlinear eigen-problem
The authors study a generalized eigenvalue problem of very special structure: \(A x + F(x) = l x\). This problem arises in the discretization of the Gross-Pitaevskii equation from physics. The matrix \(A\) is a Stieltjes matrix. The eigenvalue problem is reformulated as a fixed point problem and consequently Newton iteration may be applied. If the inital vector of the iteration is chosen from given data from the eigenvector corresponding to the positive eigenvalue of the matrix \(A\) the Newton iteration converges.
- University of Connecticut United States
Numerical Analysis, Algebra and Number Theory, fixed point problem, nonlinear eigen-problem, Numerical solution of nonlinear eigenvalue and eigenvector problems, eigenvector, Newton algorithm, Newton method, global monotone convergence, Discrete Mathematics and Combinatorics, Stieltjes matrix, Geometry and Topology, positive eigenvalue, Gross-Pitaevskii equation, Stieltjes matrices
Numerical Analysis, Algebra and Number Theory, fixed point problem, nonlinear eigen-problem, Numerical solution of nonlinear eigenvalue and eigenvector problems, eigenvector, Newton algorithm, Newton method, global monotone convergence, Discrete Mathematics and Combinatorics, Stieltjes matrix, Geometry and Topology, positive eigenvalue, Gross-Pitaevskii equation, Stieltjes matrices
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