Singular quadratic eigenvalue problems: linearization and weak condition numbers

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations coefficients may have an arbitrarily bad effect on accuracy. However, it has been known for a long time such are exceptional and standard solvers, as QZ algorithm, tend to yield good accuracy despite inevitable presence roundoff error. Recently, Lotz Noferini quantified this phenomenon introducing concept $$\delta $$ -weak condition numbers. In work, we consider quadratic two popular linearizations. Our results show correctly chosen linearization increases numbers only marginally, justifying use these linearizations in solvers also case. We propose very simple but often effective algorithm computing well-conditioned eigenvalues adding random coefficients. prove number is, with high probability, reliable criterion detecting excluding spurious created from part.