Rectified approximations for the solution of nonlinear equations |
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Authors: | Shlomo Breuer Gideon Zwas |
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Institution: | Department of Applied Mathematics, Tel-Aviv University, Tel-Aviv, Israel |
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Abstract: | In this paper we introduce the ‘rectification method’ for the construction of algorithms of pre-designed order r for the solution of nonlinear equations f(x) = 0. Our method is based upon the derivation of a rectified approximation g(x) to f(x), via Padé formulas, such that the application of the Newton-Raphson iterations to g generates the desired rth order algorithm. Various properties of g are explored as are recursive relations among rectified approximations associated with successive orders of convergence. It is demonstrated that the use of g in favor of f can relax standard sufficient conditions assuring convergence of the iterations. |
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Keywords: | Rectified approximations rootfinding |
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