Your comments

Thanks for the response! And sorry for not having answered your questions sooner!


- Is there simple example of quadratic eigenvalue problem to demonstrate the need for high-precision (e.g. where double precision fails due ill-conditioning, etc.)?

Yes, smashingly. In the NLEVP library (can be downloaded from Tisseur's website using the link you posted in your last reply), there is a famous quadratic eigenvalue problem called 'damped beam' as it is highly ill-conditioned.

- In general, what kind of applied & research problems would high-precision "quadeig" enable scientists to solve?

On the one hand, there are a large number of problems like 'damped beam' from engineering and other disciplines which are of ill-condition and, therefore, could benefit from extended precision computing by obtaining much more accurate or at least meaning results. On the other hand, people need extended precision arithmetic to generate reliable results for their research (for comparison purposes).

- Are these kind of quad-eig problems common (in research and in applications)?

Yes. Otherwise, you wouldn't have seen so many citations of Tisseur's papers (and papers by many others too) on quadratic eigenvalue problems and the NLEVP library.

- What codes researchers in the field are using now? (e.g. Francoise Tisseur's library:https://www.maths.manchester.ac.uk/~ftisseur/misc/)

It is indeed the code on this webpage that are mostly used/cited in the research of quadratic eigenvalue problems.

Thanks for the hint, buddy. The fact that the zero-padding takes place in the binary format instead of decimal totally slipped off my mind. Again, really appreciate!

Without `quadeig` is supported, the toolbox is scarcely useful for a large number of people who work on quadratic eigenvalue problems.