Modifications of parameter regula falsi method p-RF for inclusion of zero of a function with one real variable

The main objective of this thesis is to find a zero of a function using interval analysis approach. Specifically, the focus is on the well-known method called interval parameter regula falsi method (p-RF). Three modifications had been made in order to improve the p-RF method. The new modifications namely p-RFM1, p-RFM2 and p-RFM3 methods were described widely in this thesis. This study also considers the average of central processing unit (CPU) time of the algorithms of the modified methods where they were ran on Matlab R2007a software in associated with Intlab package. The theoretical analysis of the convergence rate of the modi¯ed methods were given. The p-RFM1 method is focusing on updating the midpoint of current interval in the inner iteration i. Another inner iteration l was introduced in p-RFM1 and the name of this modification is p-RFM2 method. The calculation of the gradient of the function in the p-RFM1 method is approximated using the secant method. The actual gradient of the current midpoint is now replacing the approximated gradient. The modification was named as the p-RFM3 method. All the modified methods mentioned above showed better rate of convergence than p-RF method. This is supported by lesser average CPU times tested on nine test problems. Therefore, it is concluded that the modified methods are better in term of rate of convergence and average CPU time than the original method.

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