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DTSTART;VALUE=DATE:20110510T171500
DTEND;VALUE=DATE:20110510T171500
UID:5630@agenda.unifr.ch
DESCRIPTION:It is well known that Francis' QR algorithm for computing eigenvalues\nemerged from Rutishauser's LR algorithm, but it is less obvious how\nRutishauser discovered the matrix interpretation of his qd algorithm,\nwhich is just the LR algorithm for tridiagonal matrices, and it is\nfar from obvious how he discovered the qd algorithm in the first place.\nThere are various ways to derive the latter and to detect its\nproperty of approaching eigenvalues of the matrix.\nRutishauser was well educated in classical complex analysis, and he\nbuilt on previous independent work of Hadamard and Aitken.\nStiefel provided another elegant derivation based on continued\nfractions.  And at some point Rutishauser must have realized that\nhis rhombus rules of the progressive qd algorithm can be viewed as\nLR transformation of a tridiagonal matrix.\n<br />\nReferences: Martin H. Gutknecht and Beresford N. Parlett. From qd to LR and QR, or, How were the qd and LR algorithms discovered? IMA J. Numer. Anal., advanced access, May 27, 2010.\n<br />\n[Invited by Prof. Jean-Paul Berrut]
SUMMARY:Prof. Dr. Martin GUTKNECHT (ETHZ): From qd to LR and QR
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5630
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