Metode zveznega nadaljevanja za večparametrične probleme lastnih vrednosti : doktorska disertacija
Plestenjak, Bor
Obravnavamo algebrajski večparametrični problem lastnih vrednosti ▫$W$▫ oblike ▫$$W_i(\vec{\lambda}) = \sum_{j=1}^{k}\lambda_jV_{ij}x_i - V_{i0}x_i, \quad i=1,...,k, \quad (k\ge2)$$▫, kjer je ...▫$\vec{\lambda} = (\lambda_1,\dots ,\lambda_k) \in \mathbb C^k$▫, ▫$V_{ij}$▫ pa so linearni operatorji na Hilbertovem prostoru ▫$S_i$▫. Predstavljeni sta dve novi numerični metodi za reševanje algebrajskega večparametričnega problema ▫$W$▫, obe pa temeljita na metodi zveznega nadaljevanja. Prva metoda je namenjena za reševanje simetričnega desno definitnega dvoparametričnega problema, i.e. problema, kjer so vse matrike ▫$W_{ij}$▫ realne in simetrične, operatorska determinanta pa je pozitivno definitna. Z drugo metodo lahko rešujemo simetrični šibki eliptični dvoparametrični problem ▫$W$▫, i.e. problem, kjer so vse matrike ▫$W_{ij}$▫ realne in simetrične, operatorska determinanta pa ima vsaj en pozitivno definiten kofaktor. Od preostalih numeričnih metod, ki so na voljo za večparametrični problem ▫$W$▫, se novi metodi razlikujeta v tem, da sta uporabni za splošnejše primere. Na koncu obravnavamo še stabilnost invariantnih podprostorov večparametričnega problema.
Type of material - dissertation
Publication and manufacture - Ljubljana : [B. Plestenjak], 1999
Central Technological Library of the University of Ljubljana
52047/1211 Skladišče IN: 320010181
available - outside loan, loan period: 14 days
FMF, Mathematical Library, Lj.
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