Behaviour of IRA Iterations for Derogatory and Defective Matrices

Abstract

The Implicitly Restarted Arnoldi (IRA) method is used for construction of the sequence of Krylov subspaces which converges to an invariant subspace associated with a few small wanted eigenvalues of a matrix. The convergence theorems are formulated and the construction of an invariant subspace is investigated for defective and/or derogatory matrices.

Keywords

• Behaviour
• Iterations
• Derogatory
• Defective
• Matrices