An Weighted Iterative Formula Based on[1/n]Padé Approximants
In the field of rational function approximation,Padé approximation is a classical algorithm for finding the roots of nonlinear e-quations or systems of equations.In this paper,based on the iterative algorithms constructed by Padé approximation of[1/0],[1/1]and[1/2]order,three types of iterative algorithms with parameters are obtained and convergence analysis is performed by increasing the exponential weights and applying Taylor series expansion.It is verified by numerical examples that the iterative formulas obtained for spe-cific values of parameters converge is faster than the Padé approximation and can effectively control the divergence around the repeated roots.The algorithm is more valuable in engineering calculations.
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