New zero-finding methods based on double
intercept form of a straight line

Abstract. This paper deals with quadratically convergent zero-finding methods based on double intercept form of a straight line. Hybrid zero-finding method performs better across different situations as compared to individual methods. Further, we extend hybrid approach to solve various nonlinear systems. This scheme provides advantage in the cases where the Newton's iteration process may not converge or even fails. Further, local as well as semi-local convergence analysis is done for the proposed methods. The main idea for the local convergence analysis is to estimate the bounds on convergence domain as well as the error approximations of the iterates. Depending upon the choice of initial estimate in the given domain, the semilocal convergence analysis is proved, which ensures the convergence of iterates to a unique solution in that domain.