On the Convergence Rate of Symmetric Single-Step Method ISS for Simultaneous Bounding Polynomial Zeros
نویسندگان
چکیده
A new modified method ISS for the simultaneous bounding all the zeros of a polynomial is formulated in this paper. The efficiency of this method is measured on the CPU times and the number of iterations after satisfying the convergence criteria where the results are obtained using five tested polynomials. The R-order of convergence of this method is at least 9. Mathematics Subject Classification: 65B99, 65G40
منابع مشابه
The Point Zoro Symmetric Single-Step Procedure for Simultaneous Estimation of Polynomial Zeros
The point symmetric single step procedure PSS1 has R-order of convergence at least 3. This procedure is modified by adding another single-step, which is the third step in PSS1. This modified procedure is called the point zoro symmetric single-step PZSS1. It is proven that the R-order of convergence of PZSS1 is at least 4 which is higher than the R-order of convergence of PT1, PS1, and PSS1. Hen...
متن کاملOn the Interval Zoro Symmetric Single-step Procedure for Simultaneous Finding of Polynomial Zeros
The aim of this paper is to present the interval zoro symmetric singlestep procedure IZSS1 which is the modification of interval symmetric single-step procedure ISS1. This procedure has a faster convergence rate than does ISS1. We start with suitably chosen initial disjoint intervals where each interval contains a zero of a polynomial. The IZSS1 method will produce successively smaller interval...
متن کاملGlobal convergence of an inexact interior-point method for convex quadratic symmetric cone programming
In this paper, we propose a feasible interior-point method for convex quadratic programming over symmetric cones. The proposed algorithm relaxes the accuracy requirements in the solution of the Newton equation system, by using an inexact Newton direction. Furthermore, we obtain an acceptable level of error in the inexact algorithm on convex quadratic symmetric cone programmin...
متن کاملImproved Higher Order Method for the Inclusion of Multiple Zeros of Polynomials∗
Starting from a suitable fixed point relation and employing Schröder’s and Halley-like corrections, we derive some high order iterative methods for the simultaneous inclusion of polynomial multiple zeros in circular complex interval arithmetic. These methods are more efficient compared to the existing inclusion methods based on fixed point relations. Using the concept of the R-order of converge...
متن کاملLaguerre-like Methods with Corrections for the Inclusion of Polynomial Zeros
Iterative methods of Laguerre’s type for the simultaneous inclusion of all zeros of a polynomial are proposed. Using Newton’s and Halley’s corrections, the order of convergence of the basic method is increased from 4 to 5 and 6, respectively. Further improvements are achieved by the Gauss-Seidel approach. Using the concept of the R-order of convergence of mutually dependent sequences, we presen...
متن کامل