COMPUTER TOOLS FOR SOLVING MATHEMATICAL PROBLEMS: A REVIEW

The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and contrary. The advanced hardware and modern sophistical software such as computer visualization, symbolic computation, computerassisted proofs, multi-precision arithmetic and powerful libraries, have provided resolving many open problems, a huge very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial

Convergence of simultaneous methods for determination of polynomial zeros

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 najčešće korišćenih simultanih postupaka.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

Convergence of simultaneous methods for determination of polynomial zeros

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 najčešće korišćenih simultanih postupaka.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