The Quadratic Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
Karl Meerbergen · SIAM Journal on Matrix Analysis and Applications · 2008
The quadratic Arnoldi algorithm is a Krylov method for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the second order Arnoldi (SOAR) method. In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices of linearizations in $\mathbb{L}_1$ and $\mathbb{DL}$. We also explain how to compute a partial Schur form of the underlying linearization with respect to the structure of the Schur vectors. We also formulate some open problems.