Exponentially convergent parallel algorithm for nonlinear eigenvalue problems
Ivan P. Gavrilyuk, Alexey Vladimirovich Klimenko, В. Л. Макаров, Nataliya Rossokhata · IMA Journal of Numerical Analysis · 2007
A new algorithm for nonlinear eigenvalue problems is proposed. The numerical technique is based on a perturbation of the coefficients of differential equation combined with the Adomian decomposition method for the nonlinear part. The approach provides an exponential convergence rate with a base which is inversely proportional to the index of the eigenvalue under consideration. The eigenpairs can be computed in parallel. Numerical examples are presented to support the theory. They are in good agreement with the spectral asymptotics obtained by other authors.