“…One family of particular interest is Fiedler pencils (and Fiedler matrices), introduced in [13] and since then deeply studied and generalized in many directions, see for example [2,4,7,11,30] and the references therein. Among Fiedler pencils we find, for instance, companion linearizations (the monomial analogues of the colleague), the particular Fiedler pencil analyzed in [18] (particularly advantageous for the QZ algorithm), and pentadiagonal linearizations (also potentially advantageous numerically, although currently lacking an algorithm capable to fully exploit the small bandwidth).…”