466 KB0 KB197720261982Bohte, ZvonimirGrad, Janezletnik:6številka:lstr. 43-54ISSN:0350-5596COBISSID_HOST:7534425URN:URN:NBN:SI:doc-7A7FMX8BenSlovene Society InformatikaInformatica (Ljubljana)derivative of the determinantgeneralized eigenvalue problemsLaguerre's methodLaguerrova metodamatematikamathematicsMullerjeva metodaMuller's methodNewtonova metodaNewton's methodnumerical analysisnumerična analizaodvod determinanteposplošeni problem lastnih vrednostiAlgorithms for the solution of the generalized eigenvalue problem|In this paper we deal with generalized eigenvalue problem of matrix ?$A(z)$? with elements which are polynomials of ?$z$?. The well known iterative methodsof Muller, Newton and Laguerre for finding the zeros of function ?$f(z) = {\rm det} A(z)$? are analyzed. Decompositions of the matrix ?$A(z)$? and its derivatives are introduced in order to simplify the computations of the values of ?$f(z)$? and its first and second derivatives. Comparative analysis gives some indicators about the rate of convergence, computer time and accuracy of the computed eigenvalues for each of the method used. The analysed methods proved generally to be stable, economical and easily applicable. Fortran subroutines and an example of main calling programme are added for Muller's and Laguerre's method which proved tyo be more efficient than Newton'sObravnavamo numerično reševanje posplošenega problema lastnih vrednosti za matriko ?$A(z)$? z elementi, ki so polinomi spremenljivke ?$z$?. Primerjane so dobro znane iterativne metode Mullerja, Newtona in Laguerra za računanje ničel polinoma ?$f(z) = {\rm det} A(z)$?. Vrednosti polinoma ?$f(z)$? in njegovih odvodov so izračunane na osnovi razcepa matrike ?$A(z)$?. Primerjava metod daje vpogled v hitrost konvergence, porabljen računski čas in natančnost izračunanih lastnih vrednosti za vsako metodo posebej. Analizirane metode so vse računsko stabilne, ekonomične in enostavno uporabne. Podprogrami v fortranu in primer glavnega programa so dodani za Mullerjevo in Laguerrovo metodo, ki sta se izkazali za bolj učinkovito od NewtonoveTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaSlovensko društvo Informatika