Convergence of simultaneous methods for determination of polynomial zeros

Abstract

<p>Disertacija se bavi iterativnim postupcima za simultano određivanje nula polinoma. Glavna pažnja je posvećena problemu izbora početnih aproksimacija koje omogućavaju sigurnu konvergenciju razmatranih postupaka. Koristeći originalne metode zasnovano na teoremama o lokalizaciji nula polinoma i konvergenciji nizova, konstruisani su računski proverljivi početni uslovi koji garantuju konvergenciju najče&scaron;će kori&scaron;ćenih simultanih postupaka.</p>

<p>Dissertation deals with iterative methods for simultaneous determination of polynomial zeros. The main attention is devoted to the problem of the choice of initial approximations which provide a safe convergence of the considered methods. Using original methods based on suitable localization theorems for polynomial zeros and the convergence of sequences, computationally verifiable initial conditions that guarantee convergence of the most frequently used simultaneous methods are constructed.</p>