Partial Eigensolutions of Large Nonsymmetric Matrices

摘要

We propose several methods based on combinations of deflation techniques and polynomial iteration methods, for computing small invariant subspaces of large matrices, associated with the eigenvalues with largest (or smallest) real parts. We consider both Chebyshev polynomials and least-squares polynomials for the acceleration scheme and we propose a deflation technique which is a variant of Wielandt's deflation that does not require the left eigenvectors of the matrix. As an application we compare our methods on an example issued from a bifurcation problem and show their efficiency when the number of eigvenvalues required is small.