A KQZ algorithm for solving linear-response eigenvalue equations

AbstractWe develop a new algorithm, KQZ, for solving the generalized eigenvalue problem Mx=λLx which comes from the linear-response (LR) eigenvalue equation. In contrast to the QZ algorithm, our algorithm preserves the block structure of the pencil M-λL during the computations and only uses K-orthogonal transformations. We accelerate the convergence by using a quadruple implicit-shift technique based on the implicit KQ theorem. The KQZ algorithm saves about half the computational cost and storage of the QZ algorithm