Modified algorithms in interval symmetric single-step procedure for simultaneous inclusion of polynomial zeros

Several modifications have been introduced in order to improve the problems in finding the zeros of polynomial simultaneously. They are named as Interval Symmetric Single-step 5-Delta procedure (ISS1-5D), Interval Midpoint Symmetric Single-step 5-Delta procedure (IMSS1-5D), Interval Zoro Symmetric Single-step 5-Delta procedure (IZSS1-5D) and Interval Midpoint Zoro Symmetric Single-step 5-Delta procedure (IMZSS1-5D) which were explained in details in this thesis. These four new procedures have been established from the previous symmetric single-step procedure. Furthermore, we ensure that we start by choosing the suitable initial disjoint intervals which are guaranteed to contain one zero inside of each interval. The numerical results are given to validate the new modifications and the performances are being compared with the existing procedures in terms of number of iteration and computational time (CPU times). In addition, the convergence properties for all new modifications are investigated to ensure that the procedures are useful for finding the zeros of polynomial. The convergence analysis of each procedure is also discussed. The programming codes are developed and implemented using Matlab R2012b incorporated with Intlab V5.5 toolbox and compared with the existing procedures. The efficiency of the procedures is justified by the numerical results given. The results generated showed that these new procedures produced less computational time, higher rate of convergence and achieved the desired accuracy.

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