SIAM Journal on Matrix Analysis and Applications vol:30 issue:4 pages:1463-1482
We present the Q-Arnoldi algorithm, which is an Arnoldi algorithm for the
solution of the quadratic eigenvalue problem
that exploits the structure of the linearized problem.
This allows us to reduce the memory requirements by about a half.
We compare the Arnoldi and Q-Arnoldi
algorithms by a theoretical analysis and numerical examples.
We study the application of the algorithm on the solution of the quadratic
eigenvalue problem, and explain how we can keep the structure of the Schur
vectors in the linearization.