Some Modification on Interval Symmetric Single-Step Procedure for Simultaneous Inclusion of Real Zzeros of Polynomials

In this thesis, we discuss about the interval iterative procedures of bounding real zeros of polynomials simultaneously. We concentrate on the procedure that has been proposed by Monsi in 1988 that is the interval symmetric single-step procedure ISS1 and do some modifications on the procedure and come out with three modified procedures. For these procedures, we start with suitably chosen initial disjoint intervals where each interval contains a zero of a polynomial. These procedures will produce successively smaller intervals that are guaranteed to still contain the zeros. In order to assure that the procedures are promising, we analyze the R-order of convergence of the procedures and compare them with the original procedure ISS1. We include the analysis of inclusions to certify the convergences of the procedures. The coding for the algorithms of these procedures are developed and implemented using the MATLAB R2007a in co-operated with the Intlab V5.5 toolbox for interval arithmetic developed by Rump. These three new modified procedures are proved to have better rate of convergences and this is supported by lesser CPU times and lesser number of iterations.

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