A Backward Stable Algorithm for Quadratic Eigenvalue Problems
Linghui Zeng, Yangfeng Su · SIAM Journal on Matrix Analysis and Applications · 2014
We present a backward stable algorithm for dense quadratic eigenvalue problems. Our algorithm incorporates a tropical-like scaling, a strategy for choosing linearizations, and an associated strategy for recovering eigentriples. We prove that the growth factor in the translation from conditioning for the quadratic to conditioning for the linearization and the growth factor in the translation from backward error for the linearization to backward error for the quadratic are both of order one in the algorithm.