A reduction algorithm for matrices depending on a parameter

In this articlc, \ve study square matrices pcrturbcd by a pararncter E. An efficient algorithm conlputing the z-espansiou of the eigcnvalucs in forinal Laurent-Puiseux series is provided, for \vhicli the computation of the characteristic polynomial is not rccluired. 15;e show 110~ to reduce the init,ial mat.ris so t.hat. the Lidskii-Edelman-Yla perturbat,iou theory [16] can be applied. We also explain why this approach lnily simplify t,he pcrturbcd cigenvcctor problem. The implement,ation of the algorithm in the comput.er algebra syst.em X~APIX has been used in a quantun~ mechani& cont.est to diagonalize sonle perturbed ruat.riccs and is available.

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