A Jacobi-Davidson type method for the two-parameter eigenvalue problem
Hochstenbach, Michiel E. ; Košir, Tomaž, 1962- ; Plestenjak, Bor
Predstavljena je nova numerična metoda za računanje lastnih vrednosti in lastnih vektorjev dvoparametričnega problema lastnih vrednosti. Metoda ne potrebuje dobrih začetnih približkov. Z njo pa se ...lahko lotimo tudi velikih problemov, ki so prezahtevni za obstoječe metode. Nova metoda uporablja dvostranski pristop in je posplošitev Jacobi-Davidsonove metode za desno definitni dvoparametrični problem. Tu obravnavamo veliko širši razred nesingularnih problemov. V vsakem koraku najprej izračunamo Petrovove trojice manjšega projiciranega dvoparametričnega problema, potem pa razširimo levi in desni iskalni podprostor s približnimi rešitvami ustreznih korekcijskih enačb. S pomočjo selekcije je možno izračunati tudi več kot en lastni par. Predstavljenih je tudi nekaj numeričnih primerov.
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