A restarted Induced Dimension Reduction method to approximate eigenpairs of large unsymmetric matrices

Background • The IDR(s) was introduced for solving linear systems in [3]. • IDR(s) creates residual vectors in the nested and shrinking subspaces Gj defined as Gj ≡ (A− μjI)(Gj−1 ∩ P⊥) j = 1, 2, . . . where P ∈ Cn×s and G0 ≡ C; in order to extract the approximated solution. • First IDR(s) method to solve Eq. (1) was proposed by M. H. Gutknecht and J.-P. M. Zemke [2]. The work we present here is an extension of [1].