A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Spectral methods in MatLab
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Locking and Restarting Quadratic Eigenvalue Solvers
SIAM Journal on Scientific Computing
A Jacobi-Davidson-type projection method for nonlinear eigenvalue problems
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Introduction to Data Mining, (First Edition)
Introduction to Data Mining, (First Edition)
The Conditioning of Linearizations of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Symmetric Linearizations for Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Backward Error of Polynomial Eigenproblems Solved by Linearization
SIAM Journal on Matrix Analysis and Applications
Optimal Scaling of Generalized and Polynomial Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
A block Newton method for nonlinear eigenvalue problems
Numerische Mathematik
Continuation of Invariant Subspaces for Parameterized Quadratic Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
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The simulation of drift instabilities in the plasma edge leads to cubic polynomial PDE eigenvalue problems with parameter dependent coefficients. The aim is to determine the wave number which leads to the maximum growth rate of the amplitude of the wave. This requires the solution of a large number of PDE eigenvalue problems. Since we are only interested in a smooth eigenfunction corresponding to the eigenvalue with largest imaginary part, the Jacobi-Davidson method can be applied. Unfortunately, a naive implementation of this method is much too expensive for the large number of problems that have to be solved. In this paper we will present a multilevel approach for the construction of an appropriate initial search space. We will also discuss the efficient solution of the correction equation, and we will show how optimal scaling helps to accelerate the convergence.