A two-directional Arnoldi process and its application to parametric model order reduction

We consider a two-directional Krylov subspace K k ( A [ j ] , b [ j ] ) , where besides the dimensionality k of the subspace increases, the matrix A [ j ] and vector b [ j ] which induce the subspace may also augment. Specifically, we consider the case where the matrix A [ j ] and the vector b [ j ] are augmented by block triangular bordering. We present a two-directional Arnoldi process to efficiently generate a sequence of orthonormal bases Q k [ j ] of the Krylov subspaces. The concept of a two-directional Krylov subspace and an Arnoldi process is triggered by the need of a multiparameter moment-matching based model order reduction technique for parameterized linear dynamical systems. Numerical examples illustrate computational efficiency and flexibility of the proposed two-directional Arnoldi process.