Comparative Study of Various Iterative Numerical Methods for Computation of Approximate Root of the Polynomials

The aim of this article is to present a brief review and a numerical comparison of iterative methods applied to solve the polynomial equations with real coefficients. In this paper, four numerical methods are compared, namely: Horner’s method, Synthetic division with Chebyshev method (Proposed Method), Synthetic division with Modified Newton Raphson method and Birge-Vieta method which will helpful to the readers to understand the importance and usefulness of these methods.

Inverse Multiscale Discrete Radon Transform by Filtered Backprojection

The Radon transform is a valuable tool in inverse problems such as the ones present in electromagnetic imaging. Up to now the inversion of the multiscale discrete Radon transform has been only possible by iterative numerical methods while the continuous Radon transform is usually tackled with the filtered backprojection approach. In this study, we will show, for the first time, that the multiscale discrete version of Radon transform can as well be inverted with filtered backprojection, and by doing so, we will achieve the fastest implementation until now of bidimensional discrete Radon inversion. Moreover, the proposed method allows the sacrifice of accuracy for further acceleration. It is a well-conditioned inversion that exhibits a resistance against noise similar to that of iterative methods.

Improving Graph-based methods for computing qualitative properties of markov decision processes

<span>Probabilistic model checking is a formal verification method, which is used to guarantee the correctness of the computer systems with stochastic behaviors. Reachability probabilities are the main class of properties that are proposed in probabilistic model checking. Some graph-based pre-computation can determine those states for which the reachability probability is exactly zero or one. Iterative numerical methods are used to compute the reachability probabilities for the remaining states. In this paper, we focus on the graph-based pre-computations and propose a heuristic to improve the performance of these pre-computations. The proposed heuristic approximates the set of states that are computed in the standard pre-computation methods. The experiments show that the proposed heuristic can compute a main part of the expected states, while reduces the running time by several orders of magnitude.</span>

On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations

In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed.

Combinatorial Algorithm In Linear Model

Gauss-jacobi combinatorial algorithm is an alternative approach to traditional iterative numerical methods, which is primary oriented for parameter estimation in nonlinear models. The combinatorial algorithm is often exploited for outlier diagnosis in nonlinear models, where the other parameter estimation methods lose their efficiency. The paper describes comparison of both of gauss-jacobi combinatorial and gauss-markov models executed on parameter estimation process of levelling network for the reason to find the efficiency of combinatorial algorithm in simply linear model.